# Conditional probability for OCR A-level Maths

1. Conditional probability and tree diagrams
2. Conditional probability and Venn diagrams
3. Conditional probability and two-way tables
4. Conditional probability formula

Tree diagrams can be used to model conditional probability. Conditional probability in tree diagrams can be spotted when the probability for the same outcome changes after the first branch, ie. The probability of an event occuring changes given the event that has occurred before it.

The frequencies and probabilities given on a Venn diagram can be used to calculate conditional probabilities.

Two-way tables can be used to calculate conditional probabilities.

Conditional probability is the probability of an event occurring given that another event occurs. The notation of conditional probability is P(A|B). It can be calculated by using the following formula: P(A|B) = P(A∩B)/P(B). If two events are mutually exclusive, P(A∩B) = 0, therefore P(A|B) = 0. If two events are independent, P(A) = P(A|B) and P(B) = P(A|B).

# 1

A marble is randomly drawn from the given bag. Calculate the probability that the marble is red, given that the marble is red or blue.

P(red or blue) = 12/17.
P(red|red or blue) = (6/17)/(12/17) = 1/2.

# 2

A group of 20 customers of a pet shop are asked whether they own pets or not and if they prefer dogs or cats. The data collected from the survey is represented in the given table. Calculate the probability that someone owns a pet, given that they prefer cats.

P(pet|cats) = 3/4.

# 3

Fifteen students are asked whether they are involved with Music or Drama. The results of the survey are given in the Venn diagram. Calculate the probability a student is involved with only Drama given that they are involved with Drama.

Number of students involved with Drama = 5 + 4 = 9.
P(only Drama|Drama) = 5/9.

# 4

A deck of 52 cards is made up of an equal number of red and black cards. Two cards are drawn without replacement. Construct a tree diagram to represent these events with corresponding probabilities.

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# 5

The number of female and male students in a Science and English class are counted. The data collected is presented in the given table. Calculate the probability that a student is an English student, given they are a male.

P(English|male) = 5/18.

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