Question

discrete math

1. Suppose that three friends, all heavy smokers, each have a 50-50 chance of developing lung cancer (a) Tracking whether each of the friends develops hung cancer, write down the sample space by listing its elements. Be clear about any notation that you choose to use. (b) What is the probability that exactly one of the friends develops lung cancer? (c) What is the probability that at least two of the friends develop lung cancer? 2. Six people attend the theater together and sit in a row with exactly six seats. (a) In how many ways can they be seated together in the row? (b) Suppose one of the six is a doctor who must sit in a specific aisle seat in case she is paged. How many ways can the people be seated together in the row with the doctor in the aisle seat? (e) Suppose the six people consist of three married couples and each couple wants to sit next to each other. In how many ways is this possible if the husband must sit to the left of their wife? (d) Suppose the six people consist of three married couples and each couple wants to sit next to each other. In how many ways is this possible if all the couples care about is sitting next to each other (in either order)? (e) If the six people consist of three married couples, but all six are randomly assigned the seats in the row, what is the probability that everyone gets to sit next to their spouse? 3. A study was done to determine the efficacy of three different drugs-A, B and C-in relieving headache pain. Over the period covered by the study, 80 subjects were given the chance to use all three drugs. The following results were obtained: 46 reported relief from drug A. 39 reported relief from drug B. 34 reported relief from drug C. 25 reported relief from both drugs A and B. 16 reported relief from both drugs B and C. 22 reported relief from both drugs A and C. 63 reported relief from at least one of drugs A, B or C Note that no subjects who reported relief from drug A may also have reported relief from drugs B or C. (Hint: Drawing a Venn-diagram might be helpful for this problem.) pair of these response categories are mutually exclusive. For example, some of the 46 (a) How many subjects got relief from none of the drugs? (b) How many subjects got relief from all of the drugs? (c) How many subjects got relief only from drug A? (d) How many subjects did not get relief fro, drug C? 4. Consider making a 4-letter password out of the letters from the word WHALES (with possible repeti- tion). If the letters in the password are chosen at random, what is the probability that the letter W appears at least once?

Answer 1

14 @let L, Lg and (3 is the outcome, that ist, gend or god person has long cancer. Let D,,?g and Dp is the ist, and or 3rd person do not have lung cancer. . The sample space is s={2,4g 23, 41283, L, Dg 13, 5, 2, 23, 2,D2 D3, Dilg D3, D, Dg L3, D, Pg D3} . (5) event that exactly one friend has lung cancer A={4,833, D. Lg P3, 5, 8323? a required probability=h his)

vent © event of getting at least two of the friends develop long lancer , Bg={412383, 4, 8243, Pikals, ler جاوا را * Required Probability = n(B) nis)