NIMCET 2013 Question Paper with solutions

Question : 8 of 120

Marks: +1, -0

Person A can hit a target 4 times in 5 attempts. Person B can hit a target 3 times in 4 attempts. Person C can hit a target 2 times in 3 attempts. They fire a volley. The probability that the target is hit at least two times is:

Validate

Solution:

A can hit the target 4 times in 5 attempts.
So,P (hit the target by A)

=4/5

Similarly, P (hit the target by B)

=3/4

and P (hit the target by C )

=2/3

Now, Required probability = P (target hit at-least two times)

=\;\;{4}/{5}×\;\;{3}/{4}×\;\;{1}/{3}+\;\;{4}/{5}×\;\;{1}/{4}×\;\;{2}/{3}+\;\;{1}/{5}×\;\;{3}/{4}×\;\;{2}/{3}+\;\;{4}/{5}×\;\;{3}/{4}×\;\;{2}/{3}

=\;\;{1}/{5}+\;\;{2}/{15}+\;\;{1}/{10}+\;\;{2}/{5}

[∵

AB\ov{C}+A\ov{B}C+\ov{A}BC+ABC

(atleast two times)]

=25/30=5/6

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