MCQ Questions

Question No. 1

A card is chosen randomly from a well-shuffled pack of playing cards (with no Jokers).

Answer :

a) What is the probability of choosing an Ace?

b) What is the probability of choosing a card that is not an Ace?

c) What is the probability of choosing a black court card?

d) What is the probability of choosing a card that is not a black court card?

Question No. 2

A die is rolled.

Answer :

a) Calculate the probability of getting an odd number.

b) Calculate the probability of getting a number less than 4.

c) Look at your answers to questions a) and b). You should have found that P(getting an odd number) + P(getting a number less than 4) = 1. Does this mean that ‘getting an odd number’ and ‘getting a number less than 4’ are complementary events? Give a reason for your answer.

Question No. 3

Shalewa tossed a coin five times. She got three heads and two tails. In question 1 write all probabilities as common fractions.

Answer :

a) How many different possible outcomes are there when tossing a coin?

b) How many trials took place?

c) What is the theoretical probability of getting heads when you toss a coin?

d) What was the relative frequency (experimental probability) of getting heads in Shalewa’s experiment?

Question No. 4

Bello rolled a die 10 times. He got these results: 2, 3, 3, 2, 5, 6, 4, 2, 3, 4. In question 2 write all probabilities as common fractions.

Answer :

a) How many different possible outcomes are there when rolling a die?

b) How many trials took place?

c) What is the theoretical probability of getting a 2 when you roll a die?

d) What was the relative frequency of getting a 2 in Bello’s experiment?

e) What is the theoretical probability of getting a 1 when you roll a die?

f) What was the relative frequency of getting a 1 in Bello’s experiment?

g) What is the theoretical probability of getting a 2 or a 3 when you roll a die?

Question No. 5

A group of friends played a game in which they took turns to draw a card from a standard pack of playing cards. After each draw they replaced the card and shuffled. The cards drawn were: 8♥, A♥, J♣, 4♣, 3♣, Q♥, K♦, 8♥, 2♥, 7♠, A♥, 10♥. In question 3 write all probabilities as decimal numbers, correct to two decimal places.

Answer :

a) How many different possible outcomes are there when a card is chosen from a standard pack of playing cards?

b) How many trials took place?

c) What is the theoretical probability of choosing a red card?

d) What was the relative frequency of choosing a red card in this experiment?

e) What is the theoretical probability of choosing a diamond?

f) What was the relative frequency of choosing a diamond in this experiment?

g) What is the theoretical probability of choosing a number card?

Question No. 6

Two dice are rolled.

Answer :

a) Use a two-way table to show all the possible outcomes in this sample space.

b) Explain how to find all the outcomes of which the numbers on both dice are the same.

c) Explain how to find all the outcomes of which the sum of the numbers on the dice is 7.

Question No. 7

List the sample space to show all the possible outcomes of tossing three coins. Use H for heads and T for tails.

Answer :

Question No. 8

A basket contains one red ball (R), one yellow ball (Y), one orange ball (O), one green ball (G) and one blue ball (B). One ball is taken out of the basket, its colour is noted and it is returned to the bag. Then a second ball is taken out of the basket. Use a two-way table to show all the possible outcomes in this sample space.

Answer :

Question No. 9

Sumbo is packing her school lunch. She can take one fruit juice and one sandwich. She can choose between orange juice (O) and peach juice (P). On her sandwich, she can put cheese (C), meat (M) or jam (J). List the sample space to show all the possible combinations that she can pack for her lunch.

Answer :

Question No. 10

Bisi has a ₦2 coin, two ₦1 coins and a 50 kobo coin in her pocket. She takes two coins out of her pocket at random. List the sample space to show all the possible outcomes in this situation.

Answer :

Question No. 11

Solve:

Answer :

a) Copy and complete the table.

b) One of you should toss a coin 20 times. Every time the coin comes up heads, your partner should make a note of this. Once you have tossed the coin 20 times, your partner writes the total number of heads in the second column of the table.

c) Swap roles and repeat step b). Conduct this experiment five times altogether. You should have five numbers in the second column of the table.

d) Complete the fourth column of the table. The first row will be the number of heads that you got in the first experiment. The second row will be the number of heads that you got in the first two experiments, and so on. The last row will be the number of heads that you got in all five experiments.

e) Complete the last column of the table by dividing the total number of heads in each row by the total number of tosses in that row. Write your answer as a decimal fraction, correct to two decimal places.

f) Do you agree that the probability of getting heads when you toss a coin is ½? Write this as a decimal number.

g) What do you notice about the numbers in the last column of your table? Write a sentence or two describing what you see.

Question No. 12

Calculate P(A′) if P(A) is:

Answer :

a) 0.74

b) 1/4

c) 11/50

d) 1

Question No. 13

Calculate P(B) if P(B′) is:

Answer :

a) 0

b) 6/25

c) 1/10

d) 0.59

Question No. 14

In each of the following experiments, say whether or not the events A and B are mutually exclusive.

Answer :

a) Experiment: A number from 1 to 100 is chosen at random. Event A: choosing an odd number. Event B: choosing an even number.

b) Experiment: A number between 200 and 500 is chosen at random. Event A: choosing a number between 200 and 400. Event B: choosing a number between 300 and 500.

c) Experiment: A student from an SS2 class is chosen at random. Event A: choosing a girl. Event B: choosing a boy.

d) Experiment: A student from an SS2 class is chosen at random. Event A: choosing a student whose first name begins with an A. Event B: choosing a student whose last name begins with a T.

Question No. 15

A family is planning where to go on their holidays. They have only one week, so they can only go to one destination. They have the following four options and the probability that they will go to each is given in brackets: Enugu (15%), Makurdi (25%), Beli (20%) and Lokoja (40%). Calculate the probability of each of the following.

Answer :

a) They will go to Enugu or Makurdi.

b) They will go to Beli or Lokoja.

c) They will not go to Enugu.

Question No. 16

A school held a raffle to raise money for new sports equipment. The prize was an off-road bicycle. The school sold 4 000 tickets in total. Bisola bought 25 tickets and Kole bought 40 tickets.

Answer :

a) Explain why the events (Bisola wins the prize) and (Kole wins the prize) are mutually exclusive.

b) Calculate the probability of each of the following. i) Bisola will win the prize. ii) Kole will win the prize. iii) Bisola or Kole will win the prize. iv) Neither Bisola nor Kole will win the prize.

Question No. 17

An SS2 class must choose a class captain. The following students have been nominated: Adesoji, Muyiwa, Adedolapo, Funmilola, Modupe, Ademola, Folorunso and Ajibade. The class captain will be chosen at random from these students. Calculate the probability that the name of the student who is chosen begins with:

Answer :

a) an A

b) an F

c) an M

d) an A or an F

e) an F or an M

Question No. 18

A weather forecaster noted the maximum temperatures in a certain region during a given month. The relative frequencies of the following maximum temperatures are listed in the table that follows.

Answer :

Question No. 19

Say whether or not the events A and B are independent in each of the following pairs of events.

Answer :

a) Event A: choosing an odd number between 1 and 100; Event B: choosing an even number between 1 and 100

b) Event A: choosing a team member to be the team captain; Event B: choosing a different team member to be the vice-captain

c) Event A: choosing a number between 200 and 500; Event B: choosing a different number between 200 and 500

d) Event A: choosing a library book; Event B: choosing a chapter of that book

e) Event A: choosing a friend to invite to the movies; Event B: choosing another friend to invite to the movies

f) Event A: choosing a letter of the alphabet; Event B: choosing a colour

Question No. 20

You toss a coin, roll a die and pick a card from a pack of cards (with no Jokers). Write the probability of each of the following outcomes as a fraction in its simplest form.

Answer :

a) heads, an odd number and a red card

b) heads, a number greater than 4 and a court card (Jack, Queen or King)

c) tails, a 5 and an Ace

Question No. 21

A two-digit number is formed as follows: the first digit is chosen at random from {7, 8, 9} and the second digit is chosen at random from {0, 4, 7}.

Answer :

a) Write down all possible numbers that can be formed in this way.

b) Calculate the probability that the number will be: (i) even; (ii) a multiple of 5; (iii) a multiple of 11; (iv) greater than 80; (v) less than 79

Question No. 22

A ball is chosen at random from a basket that contains only red and green balls. The probability of choosing a red ball is 5/7. Let A be the event ‘choosing a red ball’ and B be the event ‘choosing a green ball’.

Answer :

a) Explain why events A and B are complementary.

b) What is the probability of choosing a green ball?

c) If there are 8 green balls in the bag, how many balls are there altogether?

Question No. 23

In each of the following, say whether or not events A and B are independent, mutually exclusive or neither. Show all your calculations.

Answer :

a) P(A) = 0.6, P(B) = 0.3 and P(A and B) = 0.18

b) P(A) = 0.2, P(B) = 0.9 and P(A and B) = 0.6

c) P(A) = 0.1, P(B) = 0.75 and P(A or B) = 0.7

d) P(A) = 0.45, P(B) = 0.25 and P(A or B) = 0.7

Question No. 24

Three dice are rolled.

Answer :

a) What is the probability of getting three 6s?

b) What is the probability of getting anything other than three 6s?

h) What was the relative frequency of choosing a number card?

i) What is the theoretical probability of choosing a court card?

j) What was the relative frequency of choosing a court card?

k) What is the theoretical probability of choosing the Ace of hearts?

l) What was the relative frequency of choosing the Ace of hearts?

m) What is the theoretical probability of choosing a 5?

n) What was the relative frequency of choosing a 5?

Question No. 25

A simple pin code consists of a letter of the alphabet followed by a digit.

Answer :

a) How many different pin codes can be formed in this way?

b) What is the probability that a pin code, chosen at random, consists of a vowel followed by an even number?

Question No. 26

The probability that Yomi scores in a football match is 3/4, the probability that Dele scores is 2/3 and the probability that Segun scores is 3/5.

Answer :

a) P(all three players score)

b) P(Dele scores but Segun does not)

c) P(only Yomi scores)

d) P(none of them scores)

Question No. 27

In a school cafeteria, the probability that rice will be served for lunch on any given school day is 3/5, the probability that beans will be served is 1/4, and the probability that both will be served is 3/20. Let A be the event that rice will be served and B be the event that beans will be served.

Answer :

b) Are A and B independent events? Give a reason for your answer.

a) Are A and B mutually exclusive events? Give a reason for your answer.

c) Determine the probability that: i) rice will be served, but beans will not; ii) beans will be served, but rice will not; iii) neither rice nor beans will be served.

Question No. 28

In a chess tournament, Bolaji is playing against Ikeade, Sade is playing against Tola and Habib is playing against Femi. Assume that no draws will take place. The probability that Bolaji will beat Ikeade is 1/4. The probability that Sade will beat Tola is 2/3. The probability that Habib will beat Femi is 3/10.

Answer :

a) Are the following pairs of events independent, mutually exclusive, or none of the above? Give a reason to support your answer. i) Event A: Bolaji wins; Event B: Ikeade wins. ii) Event A: Sade wins; Event B: Habib wins.

b) Calculate each of the following probabilities. i) Bolaji, Sade and Habib all win. ii) Bolaji, Sade and Habib all lose. iii) Bolaji and Sade win, but Habib loses.

Question No. 29

Sola and Saheed have a bag that contains one red marble (R), one blue marble (B), one green marble (G) and one yellow marble (Y).

Answer :

a) Sola takes one marble out of the bag and then puts it back. Saheed shakes the bag well and then takes one marble out of the bag and then puts it back. (i) List all the possible outcomes in this situation. (ii) How many possible outcomes are there in this situation?

b) Saheed takes one marble out of the bag but does not put it back. Sola takes one marble out of the bag. (i) List all the possible outcomes in this situation. (ii) How many possible outcomes are there in this situation?

c) Wumi joins the game. Each child takes one marble out of the bag but does not put it back. (i) List all the possible outcomes in this situation. (ii) How many possible outcomes are there in this situation?

Question No. 30

A basket contains two red, four blue and five white balls.

Answer :

a) Three balls are taken out of the basket with replacement. What is the probability of getting: (i) three balls of the same colour (ii) three balls of different colours (iii) at least one red ball?

b) Three balls are taken out of the basket without replacement. What is the probability of getting: (i) three balls of the same colour (ii) three balls of different colours (iii) at least one red ball?

Question No. 31

Taiwo is choosing a password for a computer game. The password must be of the form @@@###, where @ is a letter of the alphabet, and # is a digit.

Answer :

a) How many different passwords can he make if he may use any letter or digit more than once?

b) If he may use any letter or digit more than once and he chooses a password at random, what is the probability that his password starts with an A and ends with a 9?

c) How many different passwords can he make if he may not use any letter or digit more than once?

d) If he may not use any letter or digit more than once and he chooses a password at random, what is the probability that his password starts with an A and ends with a 9?

Question No. 32

The infant mortality rates for Nigeria for the years from 2010 to 2013 are listed in the table below. This means that in 2010 there were 82 infant deaths for every 1 000 live births in Nigeria.

Answer :

a) What do you notice about the trend in the infant mortality rates for the years from 2010 to 2013?

b) What was the probability that a baby born alive in 2011 did not survive?

c) A couple had a baby in 2010 and another in 2013: (i) Calculate the probability that both babies were born alive but did not survive. (ii) Calculate the probability that both babies were born alive and survived.

Question No. 33

An investor has a lump sum of money to invest and he decides to invest half of his money in each of two shares on the capital market (stock exchange), X and Y. The expected performance of each share is listed in the table on the next page.

Answer :

a) Assuming that each share will perform independently of the other, calculate: (i) the probability that the investor will receive high dividends from both shares; (ii) medium dividends from both shares; (iii) low dividends from both shares; (iv) no dividends from both shares.

b) Calculate the sum of your answers in a). Explain clearly why this sum is not equal to 1.

Question No. 34

Seven men and five women took part in an ‘Esusu’ savings scheme. At the end of the first year, a random draw was held to determine which person would receive the first dividend. Let M be the event that a man’s name was drawn and W be the event that a woman’s name was drawn.

Answer :

a) Are M and W complementary, mutually exclusive or independent events? Give reasons for your answer.

b) Calculate the probability that a woman’s name was drawn. Write your answer correct to two decimal places.

Question No. 35

The population of a small village consisted of 162 men, 185 women, 259 boys and 214 girls.

Answer :

a) What was the size of the total population?

b) If one person was chosen at random from the village, calculate (i) the probability that the person was a man, (ii) a girl, (iii) an adult, (iv) a female. Write each probability correct to two decimal places.

Question No. 36

A mountain pass has been divided into four sections (A to D) for the purpose of analysis. Over the years 2011 to 2013, the number of accidents that occurred on the pass was recorded as follows.

Answer :

a) Copy and complete the table.

b) Calculate the probability that a random accident over the three-year period occurred in each of the four sections. Write your answers as percentages, correct to one decimal place.

c) Which section of the pass is most urgently in need of attention with a view to making it safer? Give a reason for your answer.

Question No. 37

The manager of a football team is planning to hire a goalkeeper. He is considering three players, Damola, Wole and Gbenga, for this position. During the past season, the probability that each goalkeeper saved any given penalty was as follows: Damola – 2/5, Wole – 1/3 and Gbenga – 11/30.

Answer :

a) Express each player’s success rate as a decimal number, correct to two decimal places.

b) Based only on this information, which player is most successful as a goalkeeper?

c) Do you think that the team manager should also take into account the number of penalties that each goalkeeper faced? Give reasons for your answer.

d) To gather more data before making a final decision, the manager tested the players with 150 penalties each. How many of these penalties would you expect each goalkeeper to save?

Question No. 38

The probability that a woman who is tested for breast cancer at a certain hospital tests positive is 5%. Of the positive tests, 8.5% are falsely positive.

Answer :

a) Calculate the probability that a woman who is tested at the hospital actually has breast cancer.

b) If 3 000 women were tested at the hospital during one year, estimate how many women: (i) tested positive; (ii) actually had breast cancer.

Question No. 39

A survey amongst a sample of 250 students revealed the following information: 55 had already visited a neighbouring country; 31 were planning to study Science at a tertiary level; 152 expected to be married before the age of 30; 198 hoped to have at least three children.

Answer :

a) Calculate the experimental probability that a student chosen at random: (i) had visited a neighbouring country; (ii) was planning to study Science at a tertiary level; (iii) expected to be married before the age of 30; (iv) hoped to have at least three children.

b) If the population from which the sample was chosen consisted of 40 000 students, predict the number of students in the population that: (i) have visited a neighbouring country; (ii) are planning to study Science at a tertiary level; (iii) expect to be married before the age of 30; (iv) hope to have at least three children.

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