# Worksheet: Complementary Events

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

**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

**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 | 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
- B
- C
- D
- E