3. A work crew is to be made up of two experts and four workers selected from a total of ve experts and six workers available. (a) How many different ways to form the work crew are possible? (b) John is one of the ve experts and Tom is one of the six workers. They are brothers. What is the probability that both brothers will be chosen? (0) What is the probability that neither will be selected? 5. A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infal- lible. In fact, it is known that 10% of the time the test gives a false negative (i.e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i.e., incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i.e., negative) result, what is the probability that she has the disease