Exam 1: Probability and Statistics 1 1. A poll conducted by a potential presiden

Question

Exam 1: Probability and Statistics 1 1. A poll conducted by a potential presidential candidate nsked two questions 1) Do vou support the candidate's position on health care? and (2) Do candidate's position on taxes? A total of 900 reponses were received to the first question and 500 said "yes" to the second. 1 200 saidno to the question and "yes" you support the to the first question, how many said no to both questions. Support your answer. 2. Two fair dice are tossed. Let A be the even that the sum of the dice is 5, and let B be the event that one die is one more than the other. Calculate P(AnBe). Su your answer. 3. Two dice are rolled. Find the probability that the first is no greater then 4 given that the sum is greater than 6. Justify your answer. 4. Holly takes a 25 question multiple choice exam where each question has four possible answers. Some of the answers she knows, and some she gets right by guessing, Suppose that the probability of her knowing the answer to a randomly selected question given that she got it right is 0.95. How many of the 25 questions was she prepared for ot:4 r Answer.

Explanation / Answer

1) from above information : below is table:

from above no to both question = total no to 2nd question -no to 2nd and yes to 1st question=(900-500)-200=200

2)there are total 4 events when sum of dice is 5 ={(1,4),(2,3),(3,2),(4,1)}

and total numebr of events in Bc = numebr of events when one die is not greater then other =number of evebts when both die shows same face ={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}

as A and Bc are mutually exclusive cause they do not share any common elements, P(AnBc) =0

1st question Yes No total 2nd Question Yes 500 No 200 total 300 900

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