John, who is 7 years old, is mapping out his future. He thinks that with probability

2/5 he might

become an astronaut (event A), with probability 1/4 he might be a basketball star (event B), and with probability 1/2 he might be happily married and have lots of children (event C). He accepts that he

can’t be an astronaut and a basketball star at the same time but thinks that astronauts and basketball

stars are just as likely as anyone else to have lots of children.

(i) Draw a Venn diagram illustrating this situation.

(ii) Calculate the probability that John has lots of children but does not get to be an astronaut

or a basketball star.

(iii) What is the probability that none of John’s dreams comes true?

[6 marks]

4. A test for a disease has probability 0.96 of giving a positive result when the disease is in fact present,

and probability 0.99 of giving a negative result when the disease is absent.

(i) About 1 in 200 adults have the disease. If a randomly selected adult is tested for the disease,

what is the probability of a positive result?

(ii) A doctor believes there is a 25% chance that his patient has the disease. The patient is tested

and the test comes up positive. What is now the probability that the patient has the disease?

[6 marks]

Help On either of these questions would be great!!!

Thanks