QJEEM19Ma4684: JEE Main 2019 Mathematics - Class 12 JEEM19Ma4684 Solution: Four persons can hit a target correctly with probabilities , ,…

Question

Verified Solution • 2025–26 Session moderate

Four persons can hit a target correctly with probabilities

{1 \over 2}

,

{1 \over 3}

,

{1 \over 4}

and

{1 \over 8}

respectively. if all hit at the target independently, then the probability that the target would be hit, is :

Accepted Answer

Let four persons are A, B, C and D.

Probablity of hitting a target by them,

P(A) =

{1 \over 2}

P(B) =

{1 \over 3}

P(C) =

{1 \over 4}

P(D) =

{1 \over 8}

Probablity of hitting target atleast once = 1 - Probablity of not hitting by anybody

P(Hit) = 1 -

P\left( {\overline A \cap \overline B \cap \overline C \cap \overline D } \right)

= 1 -

P\left( {\overline A } \right).P\left( {\overline B } \right).P\left( {\overline C } \right).P\left( {\overline D } \right)

= 1 -

{1 \over 2}.{2 \over 3}.{3 \over 4}.{7 \over 8}

=

{{25} \over {32}}

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