Filling in a Venn diagram100 people are asked if they eat meat, fish, both, or neither. You are told that 55 eat meat, 52 eat fish, and 21 eat neither. Use this information to complete the Venn diagram below.

21 eat neither

28

21

27 24

Finding probabilities

Use the Venn diagram to find the probability that someone picked at random:

a) eats meat,

b) eats fish,

c) eats neither,

d) eats only fish,

e) eats both.

‘Given that’

Given that a man eats meat, find the probability that he also eats fish.

Conditional probability

Conditional probability exists when you are given extra information, that usually results in reducing your sample space.

Formula:

probability of event A happening, given B.

probability of B, the given that part.

probability of A intersection B.

Questions

120 students in a school can opt for one or two languages for IB. 75 choose Japanese and 35 choose Chinese. 20 do neither.

a) Draw a Venn diagram to show this information.

Use your diagram to find the probability of choosing a student who,

b) takes only Japanese,

c) takes both languages,

d) takes only Japanese given that they take at least one language,

e) takes Chinese, given that they take Japanese.

Mutually exclusive

In a school of 100 boys the boys can choose to do either netball or rugby, or neither. 12 do neither, 32 do rugby and 56 do netball.Complete a Venn diagram to show this information.

What does this tell us about rugby and netball in this school?

They are mutually exclusive.

Events are mutually exclusive if:

Independence

Independent events occur when choosing one event has no effect on whether the second is chosen.

The formula is:

You also need:

1. Are events A and B independent, given that,

2. Are events A and B independent, given that,

Yes, independent No, not independent

Questions

Determine which of the events A and B are independent in each of the following questions.

3. Find x given that events A and B are independent.

Yes, independent

No, not independent