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05 Jul 2025, 21:52
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Difficulty:
45%
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Question Stats:
68% (02:17) correct
32%
(02:11)
wrong
based on 151
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Probability that a shooter misses the target is 0.8. What is the probability that in 3 shots, he hits the target at least 2 times?
(A) 0.096
(B) 0.104
(C) 0.192
(D) 0.288
(E) 0.512
(A) 0.096
(B) 0.104
(C) 0.192
(D) 0.288
(E) 0.512
avigoesforMBA
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06 Jul 2025, 00:44
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Atleast 2 times = P (Hitting 2/3 times) + P(Hitting 3 Times)
Let Hit = H, Miss = M
P(Hitting 2/3 times) = P(HHM)
But it isnt' necessary that we will hit the first 2 shots only. Hence we will use Permutations here to find no. of cases = 3!/2! = 3
P (Hitting 2/3) = 0.2 X 0.2 X 0.8 X 3 = 0.096
P (Hitting 3) = P (HHH) = (0.2)^3 = 0.008
Answer = 0.008 + 0.096 = 0.104
Let Hit = H, Miss = M
P(Hitting 2/3 times) = P(HHM)
But it isnt' necessary that we will hit the first 2 shots only. Hence we will use Permutations here to find no. of cases = 3!/2! = 3
P (Hitting 2/3) = 0.2 X 0.2 X 0.8 X 3 = 0.096
P (Hitting 3) = P (HHH) = (0.2)^3 = 0.008
Answer = 0.008 + 0.096 = 0.104
Aabhash777
General Discussion
05 Jul 2025, 22:49
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Probability of atleast 2 shots in 3 attempts translates to p(getting 2 shots in 3 attempts) + p(all three shots gotten)
2 shots in 3 attempts can take the forms - Hit Hit Lose oR Hit, Lose, Hit etc. We can get complete possibilities by 3C2 and taking care that Hit repeats itself 2 times hence (3x2)/2 = 3 possibilities of exactly 2 hits
2 Hits and a Lose = (2/10) x (2/10) x (8/10) = 32/1000 ......*
Multiply * by 3 possibilities gives 0.032 x 3 = 0.096 ............ **
Probability of all 3 wins = 0.2 x 0.2 x 0.2 = 0.008 ........... ***
Add ** and *** we get 0.096 + 0.008 = 0.104
2 shots in 3 attempts can take the forms - Hit Hit Lose oR Hit, Lose, Hit etc. We can get complete possibilities by 3C2 and taking care that Hit repeats itself 2 times hence (3x2)/2 = 3 possibilities of exactly 2 hits
2 Hits and a Lose = (2/10) x (2/10) x (8/10) = 32/1000 ......*
Multiply * by 3 possibilities gives 0.032 x 3 = 0.096 ............ **
Probability of all 3 wins = 0.2 x 0.2 x 0.2 = 0.008 ........... ***
Add ** and *** we get 0.096 + 0.008 = 0.104
