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