Handling Data 7

A bag contains 5 red counters and 3 blue counters. Two counters are taken from the bag one after the other, without replacement. What is the probability that both counters are red? Give your answer as a fraction in its simplest form.

A company has two machines, A and B, producing light bulbs. - Machine A produces 60% of the bulbs, and machine B produces 40%. - 3% of the bulbs produced by machine A are defective. - 5% of the bulbs produced by machine B are defective. A bulb is selected at random. Draw a tree diagram showing all possible outcomes and use it to calculate the probability that a randomly chosen bulb is defective.

A rare disease affects 2 out of every 1000 people. A test for the disease gives a positive result in 99% of cases when the person actually has the disease, but also gives a false positive result in 2% of cases when the person does not have the disease. If a person is selected at random and tests positive, how likely is it that they actually have the disease? Explain your reasoning.