Sherlock Holmes and John Watson were analyzing a case where the killer used an air
gun to kill the victim. The airgun used by the killer was very old and Sherlock wanted
to check whether there was any foul play or if the suspect is guilty. He wanted to
test the odds of being shot by the airgun, so he started testing by shooting balloons.
The airgun works in a special way and chances of it being hit are given as follows. An
airgun can take a maximum of 4 shots at a balloon at some distance. The
probabilities of hitting the balloon at first, second, third, and fourth shots are 0.2.0.2.
0.4, and 0.8 respectively. Can you help Sherlock to find the probability that the
balloon is hit?
0.92
0.569
O 0.842
2/45 questions attempted
Answers
Given: An airgun can take a maximum of 4 shots at a balloon at some distance.
The probabilities of hitting the balloon at first, second, third, and fourth shots are 0.2.0.2, 0.4, and 0.8 respectively.
To find : the probability that the balloon is hit
Solution:
probability that the balloon is hit = 1 - Probability that Balloon is not hit in any attempt
P hit in first = 0.2 , P did not hit in first = 0.8
P hit in second = 0.2 , P did not hit in second= 0.8
P hit in third = 0.4 , P did not hit in third = 0.6
P hit in fourth = 0.8 , P did not hit in fourth = 0.2
Probability that Balloon is not hit in any attempt = (0.8)(0.8)(0.6)(0.2)
= 0.0768
probability that the balloon is hit = 1 - 0.0768
= 0.9232
≈ 0.92
The probability that the balloon is hit is about 0.92
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