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