Conditional probability

A test consists of two sections, A and B.

85% of people pass section A.

78% of people who pass section A also pass section B.

36% of people who fail section A also fail section B.

Complete the tree diagram.

40% of people who fail at least one section take the test again. 5000 people take the test.

How many of these 5000 people are expected to take the test again?

A school year has 78 students. 28 wear glasses. of the students who wear glasses are left-handed. 30% of the students who do not wear glasses are left-handed.

ξ = students in the school year G = wears glasses L = left-handed

Complete the Venn diagram.

A left-handed student is chosen at random.

Work out the probability that the student wears glasses.

The Venn diagram shows information about 80 people who visited an online shop. ξ = 80 people T = people who bought trainers H = people who bought a hoodie

One person is chosen at random.

Work out the probability that they bought a hoodie.

One person who bought trainers is chosen at random.

Work out the probability that they bought a hoodie.

Visitors to a museum buy a child ticket or an adult ticket. Here is some information about two groups of visitors.

One visitor from each group is picked at random. Is this statement correct?

You must show your working.

The Venn diagram shows information about some houses. G = houses with a garage S = houses with a shed

A house is chosen at random.

The house has a garage. What is the probability that it has a shed?

The house does not have a garage. What is the probability that it does not have a shed?

Show that P(G ∩ S)^/ P(G U S^/)

ξ = 29 students in a class C = students who own a cat D = students who own a dog

A student is chosen at random. Circle the probability that the student owns a cat or a dog but not both.

A student who owns a dog is chosen at random. Circle the probability that the student also owns a cat.

In the Venn diagram ξ represents 31 students in a class C is students who have a cat D is students who have a dog

One student from the class is picked at random. Work out the probability that the student has a dog.

One of the students who has a cat is picked at random. Work out the probability that this student has a dog.

A school has 86 teachers. 42 are male and 44 are female. of the male teachers have blue eyes. of the female teachers have blue eyes.

ξ = teachers in the school M = male teachers B = teachers who have blue eyes

Complete the Venn diagram.

One teacher who has blue eyes is chosen at random. Work out the probability that the teacher is male.