The weather forecaster indicates that there is a 25% chance of rain on Sat- urday and a 25% chance of rain on Sunday. If the probability that it rains on both Saturday and Sunday is 10%, what is the probability that it rains over the weekend? If a registration plate for a car consists of three letters (A-Z) and three numbers (0-9), in any arrangement, what is the probability that a registration plate will contain no duplicate letters or numbers? A dart player has a 5% chance of hitting the bulls-eye each throw they make. If each throw is independent, how many throws does the player need to make to be assured of having a 50% chance of hitting the bulls-eye? Tests for diseases can sometimes be wrong, there are two types of errors that can occur; indicating a disease is present when it isnt, or failing to indicate a disease is present when it is. The table below gives some results for one such test: T+= positive test T??= negative test D+= disease present D??= no disease present D+ D Total T+ 25 14 39 T 18 78 96 Total 43 92 135 What is the probability that the disease is present given that the test is positive? What is the probability that the disease is not present given that the test is negative? Without making any changes to the test, what can be done to improve the accuracy of the testing procedure to determine that a patient either has or doesnt have the disease?
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