practice2a-solutions

practice2a-solutions - UNIVERSITY OF VICTORIA MATHEMATICS...

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Unformatted text preview: UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 SIT-DOWN PRACTICE TEST 2, NOVEMBER 19 Question 1. You roll a fair 4 sided die twice and multiply the numbers showing on the top face of each roll. What is the expected value of this experiment? (The numbers on the faces of a 4 sided die are 1 , 2 , 3, and 4). (A) (B) 1 (C) 2 (D) 3 (E) 4 (F) 5 (G) 6 (H) 7 (I) 8 (J) 9 Solution: The possible results of two rolls can be summarized by the following table: 1 2 3 4 1 1 2 3 4 2 2 4 6 8 3 3 6 9 12 4 4 8 12 16 Each of these occurs with probability 1 16 , and so summing up we find that the expected value is 100 16 = 6 . 25. So the answer is (G). Question 2. There is a game where the player flips a fair coin 6 times. If they get exactly 2 heads they must pay $4. If they get exactly 3 heads, they receive $4, and if they get exactly 4 heads they receive $12. Otherwise, they get and pay nothing. How much should they expect to win on average by playing this game repeatedly? (A)- $0 . 50 (B) $0 . 00 (C) $0 . 50 (D) $1 . 00 (E) $1 . 50 (F) $2 . 00 (G) $2 . 50 (H) $3 . 00 (I) $4 . 00 (J) $6 . 00 Solution: Let X be the random variable that counts heads. This is a binomial random variable with n = 6 trials, and the probability of a heads is p = 1 2 . Thus, the expected winnings for the player in this experiment is- $4( P ( X = 2)) + $4( P ( X = 3)) + $12( P ( X = 4)) =- $4 6 2 (0 . 5) 2 (0 . 5) 4 + $4 6 3 (0 . 5) 3 (0 . 5) 3 + $12 6 4 (0 . 5) 4 (0 . 5) 2 =- $4(15) + $4(20) + $12(15) 2 6 = $200 64 $3 . 125 ....
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This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.

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practice2a-solutions - UNIVERSITY OF VICTORIA MATHEMATICS...

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