JEE MAIN - Mathematics (2019 - 9th April Morning Slot - No. 14)
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 :
$${{25} \over {32}}$$
$${{25} \over {192}}$$
$${{1} \over {192}}$$
$${{7} \over {32}}$$
Explanation
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 - $${1 \over 2}.{2 \over 3}.{3 \over 4}.{7 \over 8}$$
= $${{25} \over {32}}$$
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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