At a shooting gallery, Alan takes shots at a moving target. His performance is affected by the weather. It is given that the probabilities of having a fine, cloudy and rainy days are 0.6, 0.3 and 0.1 respectively. When the days are fine, cloudy and rainy, the probabilities that Alan hit the target are 0.8, 0.7 and 0.4 respectively. Suppose all shots are independent.
1) Find the probability that he takes two shots with both hitting the target and it is a cloudy day.
2) Find the probability that he takes two shots with both hitting the target.
3）It is given that he takes two shots with both hitting the target. Find the probability that it is a cloudy day.
4) If it is a rainy day and he takes three shots. Find the probability that he hits the target in all shots, given that he hits the target at least one of the shots.
5) If it is a rainy day and he wants ti assure the probability of hitting the target at least once is greater than 0.9. Find the least number of shots that he must take.
Probability
2011-04-22 11:53 pm
回答 (1)
2011-04-23 2:42 am
✔ 最佳答案
(1) (0.3)(0.7)(0.7) = 0.147(2) (0.6)(0.8)(0.8) + (0.3)(0.7)(0.7) + (0.1)(0.4)(0.4) = 0.451
(3) 0.147/0.451 = 0.3259
(4) P(at least one hit)
= 1 - P(0 hit)
= 1 - (0.6)^3
= 0.784
P(at least one hit and three hits)
= P(three hits)
= 0.064
So, required probability = 0.064/0.784 = 0.08163
(5) Let the number is n
1 - (0.6)^n > 0.9
n > 4.5076
The least no. is 5
收錄日期: 2021-04-26 14:07:17
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