Question

Problem No. 53 /10 pts Larry and Sam each fire one shot at a target. Larry has probability 0.49 of hitting the target. Sam has probability 0.32. The shots are independent. 1) Find the probability that the target is hit. 2) Find the probability that the target is hit by exactly one shot. 3) Given that the target was hit by exactly one shot, find the probability that ILarry hit the target. Show your explanations Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the third decimal place where applicable.

Answer 1

P(larry) = 0.49

P(sam) = 0.32

1) P(target is hit) = P(target hit by at least one) = 1 - P(none)

= 1 - (1-0.49)*(1-0.32)

= 0.6532

So, probability that target is hit is 0.653. (rounded to 3 decimal places)

2) P(Exactly one shot) = P(Larry hit)*P(Sam missed) + P(Larry missed) * P(Sam hit)

= 0.49*(1-0.32) + (1-0.49)*0.32

= 0.4964

So, target is hit by exactly one shot is 0.496. (rounded to 3 decimal places)

3) P(Larry hit | target hit exactly one shot) =

0.3332 0.49 *(1-0.32) | 0.4964 <0.671 04964

So, probability is 0.671 that Larry hit the target given that the target was hit by exactly one shot.

Please comment if any doubt. Thank you.