A man make attempts to hit the target. The probability of h... | MATH - CONDITIONAL PROBABILITY, BAYE'S THEOREM | SolveeIt | Solveeit

Today, August 18

Question

A man make attempts to hit the target. The probability of

hitting that target is $\frac { 3 } { 5 }$ . Then the probability that A hit the

target exactly 2 times in 5 attempts, is -

A

$\frac { 144 } { 625 }$

B

$\frac { 72 } { 3125 }$

C

$\frac { 216 } { 625 }$

D

None of these

Answer

$\frac { 144 } { 625 }$

Explanation

Solution

P(Hit) = $\frac { 3 } { 5 }$ = p ; P( $\overline { \mathrm { Hit } }$ ) = $\frac { 2 } { 5 }$ = q, n = 5

P (r = 2)= ⁵C₂ $\left( \frac { 3 } { 5 } \right) ^ { 2 }$ × $\left( \frac { 2 } { 5 } \right) ^ { 3 }$ =10× $\frac { 9 \times 8 } { 25 \times 125 }$ = $\frac { 144 } { 625 }$