Laura and Phillip each fire one shot at a target, Laura has aprobability 0.5 of hitting the target, and Phillip has aprobability 0.3. The shots are independent.

a. Find the probability that the target is hit.

b. Find the probability that the target is hit by exactly oneshot.

c. Given that the target was hit by exactly one shot, find theprobabilty that Laura hit the target.

Step-by-step explanation:

Given that Laura and Phillip each fire one shot at a target, Laura has aprobability 0.5 of hitting the target, and Phillip has aprobability 0.3. The shots are independent.

a) Probability that the shot is hit

= P (either Laura hits) + P (Phillip hits) - P (both hit) (additional theorem of prob)

=0.5+0.3-0.5*0.3

= 0.8-0.15

=0.65

b) Probability that the target is hit by exactly one shot

=P (Only Laura hits) + P (Phillip only hits)

= P (Laura hits and Philip not hits) + P (Phillip hits and Laura hits)

=0.5 (0.7) + (0.5) (0.3)

=0.5

c) Prob that Laura hit the target, given that the target was hit by exactly one shot

=0.35/0/5

= 0.7