Four persons can hit a target correctly with probabilities [1 2], [1 3], [1 4] and [1 8] r…

Question

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

= $${{25} \over {32}}$$

Solutions · 1