An Olympic archer misses the bull's-eye 11% of the time. Assume each shot is independent of the others. If she shoots 9 arrows, what is the probability of each of the results described in parts a through f below? a) Her first miss comes on the seventh arrow. The probability is 0.0547 (Round to four decimal places as needed.) b) She misses the bull's-eye at least once. c) Her first miss comes on the second or third arrow. d) She misses the bull's-eye exactly 3 times. e) She misses the bull's-eye at least 3 times. f) She misses the bull's-eye at most 3 times.
Added by Christopher A.
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The problem involves a series of independent trials (shots), each with two possible outcomes: hitting or missing the bull's-eye. This is a binomial distribution problem where the probability of missing the bull's-eye (failure) is 0.11, and the probability of Show more…
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An Olympic archer misses the bull's-eye 13% of the time. Assume each shot is independent of the others. If she shoots 9 arrows, what is the probability of each of the results described in parts a through f below? a) Her first miss comes on the fourth arrow. The probability is 9.8. (Round to four decimal places as needed.) b) She misses the bull's-eye at least once. The probability is 0.6731. (Round to four decimal places as needed.) c) Her first miss comes on the second or third arrow. The probability is nothing. (Round to four decimal places as needed.) d) She misses the bull's-eye exactly 3 times. The probability is nothing. (Round to four decimal places as needed.) e) She misses the bull's-eye at least 3 times. The probability is nothing. (Round to four decimal places as needed.) f) She misses the bull's-eye at most 3 times. The probability is nothing. (Round to four decimal places as needed.)
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An Olympic archer misses the bull's-eye 15% of the time. Assume each shot is independent of the others. If she shoots 7 arrows, what is the probability of each of the results described in parts a through f below? The probability is 0.6794. (Round to four decimal places as needed.) c) Her first miss comes on the second or third arrow. The probability is .2359. (Round to four decimal places as needed.) d) She misses the bull's-eye exactly 3 times. The probability is . (Round to four decimal places as needed.)
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Probability of Hitting a Target The probability that an archer hits the target is $p=0.9,$ so the probability that he misses the target is $q=0.1 .$ It is known that in this situation the probability that the archer hits the target exactly $r$ times in $n$ attempts is given by the term containing $p^{\prime}$ in the binomial expansion of $(p+q)^{n}$ . Find the probability that the archer hits the target exactly three times in five attempts.
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