3 A dart player has a 5 chance of hitting the bullseye each

3. A dart player has a 5% chance of hitting the bull?s-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 bull?s-eye? 4. Tests for diseases can sometimes be wrong, there are two types of errors that can occur; indicating a disease is present when it isn?t, or failing to indicate a disease is present when it is. The table below gives some results for one such test: (a) What is the probability that the disease is present given that the test is positive? (b) What is the probability that the disease is not present given that the test is negative?

Solution

3.Each throw is independent and has 5% chance of hitting.

Thus, to be assured to have 50% chance the player needs to make at least 50/5=10 throw.

4.a.The probability that the disease is present given that the test is positive is:

25/39=0.64

b.The probability that the disease is not present given that the test is negative is:78/96=0.8125