Abby, Deborah, Mci-Ling, Sam and Roberto work in a firm\'s relations office. The
ID: 3203728 • Letter: A
Question
Abby, Deborah, Mci-Ling, Sam and Roberto work in a firm's relations office. Their employer must choose two of them to attend a Conference in Paris. to avoid unfairness, the choice will be made by drawing two names form a hat. (This is a Simple Random Sample of size 2) In order to find the sample space you should write down all possible choices of two of the five members. a. How many pairs are there is the Sample Space? Write the sample space. b. The random drawing makes all choices equally likely. What is the probability of each choice? c. What is the probability that neither of the two men Here are the distributions of blood types for a randomly chosen person in China and in the United States: a. Choose an American and a Chinese independently of each other. What is the probability that both have type O blood? _____ b. What is the probability that both have the same blood type? ____ Two cards are drawn without replacement from an ordinary deck of 52 cards. Find the probability that the first card is a heart and the second card is red. On a typical January day in Manhattan the probability of snow is, 10, the probability of traffic jam is 80 and the probability of snow or 8 traffic jam or both is 82. Are the events it snows and the event a traffic jam occurs independent? You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 100. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is even, you win $25. If the number the ball lands on is odd, you win nothing. If you play the game, what is the expected payoff? ____ For a fundraiser, there is a raffle with 250 tickets, with 250 tickets. One ticket will win a $670 prize, and the other tickets will win nothing. If you have a ticket, what is the expected payoff? ____Explanation / Answer
19. The probability that both have type O blood groups is 0.35*0.45 = 0.1575
20. a) The probability that both have the same blood type is 0.35*0.45 + 0.27*0.4 + 0.26*0.11 + 0.12*0.04 = 0.2989
b). The probability that the first card is heart and the second card is red is
(13/52) * (25/52) = 325/2704 = 0.1202
21. Let A denote snow , B denote traffic Jam
P(A and B) = P(A) + P(B) - P(A or B)
= 0.10 + 0.80 - 0.82 = 0.08
P(A) P(B) = 0.10*0.80 = 0.08
Here P(A and B) = P(A)P(B)
Therefore, A and B are independent
22. E(number of complaints per day) = 0*0.01 + 1*0.05 + 2*0.15 + 3*0.26 + 4*0.33 + 5*0.14 + 6*0.06 = 3.51
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