# Conditional Probability

## Find the probability of one event happening given that another event has already happened.

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This is level 1: a mixed selection of conditional probability questions. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

 1 In a bookstore, there are two sections: fiction and non-fiction. In the fiction section, 80% of the books have hard covers, while in the non-fiction section, only 40% of the books have hard covers. If a customer picks a book at random and it has a hard cover, what is the probability that it is from the non-fiction section? Assume that there are an equal number of books in the fiction and non-fiction sections. Give your answer to three significant figures. ☐ ☐ ✓ ✗ 2 29 Scouts went hiking. 10 got lost, 14 got blisters, and 5 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost. Give your answer as a fraction. ☐ ☐ ✓ ✗ 3 Every family in Happyland has either has a car or a motor scooter or both. 72% of the families have a car. 89% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter. Give your answer as a fraction. ☐ ☐ ✓ ✗ 4 Box A contains 6 red and 8 blue cubes, and box B contains 10 red and 12 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B? Give your answer as a fraction. ☐ ☐ ✓ ✗ 5 What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 9% chance and machine B has a 13% chance of breaking down on any given day? Give your answer to three significant figures. ☐ ☐ ✓ ✗ 6 Each afternoon the probability my cat sleeps is 0.6 and the probability that my dog sleeps is 0.5. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon. Give your answer to three significant figures. ☐ ☐ ✓ ✗ 7 Tin A contains 6 red balls and 8 green balls. Tin B contains 10 red balls and 12 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B. Give your answer as a fraction. ☐ ☐ ✓ ✗ 8 The probability that I drop and brake my phone when I visit a coffee shop is 0.05. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred? Give your answer to three significant figures. ☐ ☐ ✓ ✗ 9 The probability that it is cloudy on a particular day is 0.2. The probability that it is cloudy with a high level of pollution on a particular day is 0.1. Find the probability that there will be a high level of pollution on a day when it is cloudy. Give your answer to three significant figures. ☐ ☐ ✓ ✗ 10 Given equal populations of Type X and Type Y bacteria, with mutation rates of 60% and 70% respectively, if a mutated bacterium is found, what's the probability it's Type Y? Give your answer to three significant figures. ☐ ☐ ✓ ✗
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## Description of Levels

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Probability - This is the basic probability set of exercises for those new to this topic.

Tree Diagrams - These diagrams can help solve certain types of conditional probability problems.

Venn Diagrams - This type of diagram is also a useful problem solving tool.

Level 1 - A mixed selection of Conditional Probability questions

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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## Conditional Probability:

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred. It represents the probability of event A happening, given that event B has already occurred. It is denoted as P(A|B), read as "the probability of A given B."

The formula for conditional probability is:

$$P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}$$

Where:

$$P(A|B)$$ is the conditional probability of event A given event B,

$$P(A \cap B)$$ is the probability of both events A and B occurring,

$$P(B)$$ is the probability of event B occurring.

## Help Video

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