Answer problem 2 and 3 with solution

2) The five interlocking Olympic rings are colored black, blue, red, green, yellow, but not necessarily in this order. Members of a class are asked to color the rings. However, as they are not given the order of the colors, each one colors at random, using the five colors. Assume that no two rings are colored the same. a. How many different ways are there of coloring the rings? b. What is the probability that there are two people who have colored the rings exactly the same way? c. The correct coloring is: blue, yellow, black, green, red. What is the probability that someone in the class will have found it? d. What is the probability that at least one color will be chosen correctly for a random coloring? e. Assume that two or more rings may be colored the same. How many different ways are there of coloring the rings? 3) About 2% of the Philippine population has breast cancer. The probability of getting a false positive result on a breast cancer test is 9%, while the probability of getting a false negative result is 18%. a. Jo, a 44-year old woman, tested positive for breast cancer. What is the probability that she has breast cancer? b. Amy, a 50-year old woman, tested negative for breast cancer. What is the probability that she has breast cancer? c. To be more certain of the result, Amy decided to take the test again. She obtained a negative result for a second time. What is the probability that she does not have breast cancer? Assume that the two consecutive tests are independent.