Question
Math 237 Exam 1 Oct.12, 2017 1. A coin is tossed 3 times. a) Write down the sample space, S b) Let E be the event "at least one tail appears in the 3 tosses" Write down E as a subset of S- ie. list all the outcomes in E c) What is PIE)? 2. A committee of 6 is chosen from a group of 6 men and 6 women. What is the probability the group contains unequal numbers of men and women? 3. Given: E and Fare events withAE)-4, P(F)',andREoh-8 a) Find P(E F). b) Are E and F independent? Why or why not? 4. Four married couples are randomly paired at a dinner table-the four women on one side of the table and the four men on the other side. What is the probability that no man sits across from his wife? 5. An insurance company classifies people as normal or accident prone. Suppose that the prone probability that a normal person has an accident is 0.2 and that for an accident person this probability is 06. Now suppose 1896·18 of the population is accident prone. If a person has no accidents, what is the probability that he or she is accident prone? 6. A bowl contains 10 chips numbered 1- 10. Two chips are randomly selected from the bowl. Determine the probability that the sum of numbers on the chips is 10 if the sampling is a) without replacement b) with replacement. 7. Three cards are randomly selected from a deck of 52 cards. What is the probability that they are all of different suits ? Note: There are 4 suits: clubs, diamonds, hearts, and spades Each suit has 13 cards: 2,3,4.,., 10, Jack, Queen, King, Ace.
Explanation / Answer
1.
(a) Let T denote tail and H denote head.
Sample space ={HHH,HHT, HTH, HTT, THH, TTH, THT, TTT}
(b) If E is even of atleast one tail appears, then
E= {HHT, HTH, HTT, THH, TTH, THT, TTT}
(c) P(E) = (number of elements in E)/ (Number of elements in S) = 7/8