# Worksheet: Complementary Events

In this worksheet, we will practice finding the probability of complementary events.

Q1:

A bag contains 6 red balls, 8 yellow ones, and 4 black ones. If a ball is randomly selected, find the probability of it being NEITHER black NOR yellow.

• A
• B
• C
• D
• E

Q2:

A class in a school contains 38 students. At the end of the school year, 28 of the students passed mathematics, 32 passed science, and 26 passed both science and mathematics. If a student is chosen at random from the class, what is the probability that they failed science?

• A
• B
• C
• D
• E

Q3:

If the probability of an event happening is , what is the probability of the event not happening?

• A
• B
• C
• D

Q4:

If the probability that a student passes an exam is , what is the probability that the student fails?

Q5:

What is the probability of the pointer landing on a section which is not green on the pictured fair spinner?

• A
• B
• C
• D

Q6:

The probability of a getting a head when flipping a biased coin is 0.56. What is the probability of getting tails when flipping the coin?

Q7:

A box contains 56 balls. The probability of selecting at random a red ball is . How many balls in the box are not red?

Q8:

If the chance of Daniel bowling a spare is 8 out of 10, determine the probability of him missing the spare.

• A
• B0
• C1
• D

Q9:

The table represents the data collected from 200 conference attendees of different nationalities:

Speak Arabic Speak English Speak French Total Sum
Man 45 35 45 125
Woman 40 30 5 75
Sum 85 65 50 200

Find the probability that a randomly selected participant does NOT speak English.

Q10:

If the chance of hitting a specific target on a dart board is , what is the probability of hitting any other target?

Q11:

If the probability that a football team wins the national league in a country is 0.254, what is the probability that the team does not win?

Q12:

Suppose and are two events. Given that the probability of or occurring is 0.67, find the probability that neither nor occurs.

Q13:

A bag contains 4 red, 3 green, 5 blue, and 9 yellow marbles. If a marble is randomly chosen from the bag, what is the probability of choosing a marble which is not blue?

• A
• B
• C
• D
• E

Q14:

The probability that a student passes their mathematics exam is 0.73. What is the probability that they fail?

Q15:

Suppose is an event with probability . Determine .

• A
• B
• C
• D

Q16:

The probability that an event occurs is . What is the probability that the event does not occur?

• A
• B
• C
• D
• E

Q17:

A survey of 48 students reveals that 28 of the students prefer playing football and 11 prefer basketball. The rest of the students prefer tennis. If a student is chosen at random, what is the probability they prefer tennis?

• A
• B
• C
• D

Q18:

A class has 45 students. The probability of choosing at random a student whose age is 10 or less is . How many students in the class are older than 11?

Q19:

A factory produces 9,000 shirts each day. At the end of a day, 500 shirts were inspected and 18 were found to be defective. What is the expected number of shirts produced that day that will not be defective?

Q20:

Suppose and are two events. Given that , , and the probability of only occurring is 0.35, find the probability that does not occur.

Q21:

According to a survey, 24 out of 120 school students prefer reading comic books. In a school of 500 students, how many are expected not to prefer comic books?

Q22:

Suppose is the sample space of a random experiment. Given that and , find .

• A
• B
• C
• D

Q23:

A coin is tossed 700 times. Given that heads appeared 353 times, how many times did tails occur?

Q24:

A survey asked 112 students from a school what sport they prefer and the results are shown in the table.

 Favourite Sport Number of Students Football Handball Athletics Tennis Basketball 27 40 9 29 7

Find the probability that a student does NOT prefer athletics. Round your answer to 3 decimal places.

Q25:

There are 18 boys in a class of 33 students. If a student is selected at random, what is the probability of the student being a boy?

• A
• B
• C
• D
• E