302 HW 16 - #31. These two outcomes are equally likely, and...

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M302 HOMEWORK #16 Dr. Schurle Assignment: page 549, #2, 5, 8, 21, 23, 26, 31, 40 Grade the following for 2 points each, with two points total for work on the remaining problems. #2. The probability that the event will NOT happen that day is 999/1000 = 0.999. The probability that the event will NOT happen two days in a row is 0.999 2 = .998001 . The probability that the event will NOT happen during an entire year is 0.999 365 = 0.6941. #23. If you roll the die just 7 times, then the probability that you will get your phone number is 1 in 10 7 , or 0.0000001. But if you roll the die 7 times, then another 7 times, then another . ..., and do this, say, 1,000,000 times, then the probability of seeing your phone number is about 1 in 10, and if you do this 10,000,000 times, then the probability is about 63% of seeing your phone number. So, if you roll often enough, the probability of seeing your phone number gets closer and closer to 1, or nearly certain.
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Unformatted text preview: #31. These two outcomes are equally likely, and one is just as random as the other, because the probability of seeing any particular exact outcome when you flip a coin 10 times is 1 in 2 10 , or 1/1024, or about 0.000976. #40. There are two possible interpretations of this question. (a) You want the probability that you will win at least once in 36 tries. The probability that you will lose in one try is 51/52, so the probability that you will lose 36 times is 51 / 52 36 = .98077 36 = 0.4971 , so the probability that you will win at least once is 1 – 0.4971 = .5029. (b) You want the probability that you lose 35 times and win exactly on the 36 th try. This probability is 51 / 52 35 × 1 / 52 = 0.5068 × 0.01923 = 0.0097. I think interpretation (a) is what is intended. Note: Answers may be rounded off more than in these solutions....
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This note was uploaded on 03/19/2008 for the course M 302 taught by Professor Irwin during the Spring '08 term at University of Texas at Austin.

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