Person A can hit a target 4 times in 5 attempts. Person B - 3 times in

1.	Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C - 2 times in 3 attempts. They fire a volley. The probability that the target is hit atleast two times is1. 3/42. 1/23. 5/64. 1
Answer» Correct Answer - Option 3 : 5/6 Concept: P(\(\bar A\) : Not hitting the target) = 1 - P(A: hitting the target ) Calculations: Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C - 2 times in 3 attempts. P(A : hitting the target ) = \(\rm \dfrac 45\) ⇒P(\(\bar A\) :Not hitting the target) = \(\rm \dfrac 15\) P(B: hitting the target) = \(\rm \dfrac 34\) ⇒P(\(\bar B\) :Not hitting the target) = \(\rm \dfrac 14\) P(C: hitting the target) = \(\rm \dfrac 23\) ⇒P(\(\bar C\) : Not hitting the target) = \(\rm \dfrac 13\) The probability that the target is hit atleast two times = \(P(A)P(B)P(\bar C)+P(A)P(\bar B)P(C) + P(\bar A)P(B)P(C) + P(A)P(B)P(C)\) ⇒ The probability that the target is hit atleast two times = \(\dfrac 15+ \dfrac 1 {10}+ \dfrac {2}{15}+ \dfrac{2}{5}\) ⇒ The probability that the target is hit atleast two times = \(\dfrac 5 6\)

Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C - 2 times in 3 attempts. They fire a volley. The probability that the target is hit atleast two times is1. 3/42. 1/23. 5/64. 1

Answer» Correct Answer - Option 3 : 5/6

Concept:

P(\(\bar A\) : Not hitting the target) = 1 - P(A: hitting the target )

Calculations:

Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C - 2 times in 3 attempts.

P(A : hitting the target ) = \(\rm \dfrac 45\)

⇒P(\(\bar A\) :Not hitting the target) = \(\rm \dfrac 15\)

P(B: hitting the target) = \(\rm \dfrac 34\)

⇒P(\(\bar B\) :Not hitting the target) = \(\rm \dfrac 14\)

P(C: hitting the target) = \(\rm \dfrac 23\)

⇒P(\(\bar C\) : Not hitting the target) = \(\rm \dfrac 13\)

The probability that the target is hit atleast two times = \(P(A)P(B)P(\bar C)+P(A)P(\bar B)P(C) + P(\bar A)P(B)P(C) + P(A)P(B)P(C)\)

⇒ The probability that the target is hit atleast two times = \(\dfrac 15+ \dfrac 1 {10}+ \dfrac {2}{15}+ \dfrac{2}{5}\)

⇒ The probability that the target is hit atleast two times = \(\dfrac 5 6\)