Worksheet: Probability of Complementary Events

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

Q1:

A bag contains 7 red balls, 6 yellow ones, and 4 black ones. If a ball is randomly selected, find the probability of it being NEITHER red NOR yellow.

  • A 6 1 7
  • B 7 1 7
  • C 1 1 1 7
  • D 4 1 7
  • E 1 3 1 7

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 6 1 9
  • B 1 6 1 9
  • C 5 1 9
  • D 3 1 9
  • E 1 4 1 9

Q3:

If the probability of an event happening is 1 1 3 0 , what is the probability of the event not happening?

  • A 1 7 3 0
  • B 3 5
  • C 2 3
  • D 1 9 3 0

Q4:

If the probability that a student passes an exam is 3 9 % , 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 1 2
  • B 3 4
  • C 5 9
  • D 5 8

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 5 7 . How many balls in the box are not red?

Q8:

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

  • A 4 5
  • B0
  • C1
  • D 1 5

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 4 9 % , 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 𝐴 and 𝐵 are two events. Given that the probability of 𝐴 or 𝐵 occurring is 0.67, find the probability that neither 𝐴 nor 𝐵 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 6 7
  • B 4 7
  • C 5 2 1
  • D 1 6 2 1
  • E 1 7

Q14:

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

Q15:

Suppose 𝐴 is an event with probability 𝑃 ( 𝐴 ) = 1 4 1 9 . Determine 𝑃 𝐴 .

  • A 4 1 9
  • B 7 1 9
  • C 1 4 1 9
  • D 5 1 9

Q16:

The probability that an event occurs is 2 1 1 . What is the probability that the event does not occur?

  • A 1 1 2
  • B 9 2
  • C 2 1 1
  • D 9 1 1
  • E 1 1 9

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 3 1 4 8
  • B 3 2 9
  • C 3 1 8 7
  • D 3 1 6

Q18:

A class has 45 students. The probability of choosing at random a student whose age is 10 or less is 2 3 . 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 𝐴 and 𝐵 are two events. Given that 𝑃 ( 𝐴 ) = 1 1 0 , 𝐴 𝐵 , and the probability of only 𝐵 occurring is 0.35, find the probability that 𝐵 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 𝑆 is the sample space of a random experiment. Given that 𝐴 𝑆 and 𝑃 𝐴 𝑃 ( 𝐴 ) = 2 3 , find 𝑃 ( 𝐴 ) .

  • A 1 3
  • B 2 3
  • C 2 5
  • D 3 5

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 Football Handball Athletics Tennis Basketball
Number of Students 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 3 2 0
  • B 5 1 1
  • C 9 5 0
  • D 6 1 1
  • E 1 1 1

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.