Question

6. Stormtroopers will hit their targets 20% of the time that they shoot. a) Ten stormtroopers shoot at Luke. Find the probability that he’s hit. b) Stormtroopers shoot at Luke in succession until he’s hit (if they miss, they’re killed instantly and a new one takes a shot). What is the probability that it takes exactly 7 stormtroopers to hit Luke? c) If Luke is hit, there’s a 60% chance that he’ll live. A stormtrooper shoots at Luke, and he survives. Find the probability that Luke was hit.

Answer 1

Quesion 6

P(Stormtroopers will hit their targets) = 0.20

(a) Number of stormtroopers = 10

P(He wil get hit) = 1 - P(He will not get by any of the shot) = 1 - (1 - 0.20)¹⁰ = 0.8926

(b) Here it is asked that the probability that exactly 7 stormtroopers to hit Luke that means 6 stormtroopers failed to hit luke and 7th one succeded.

That means probability = (1 - 0.20)⁶ * 0.2 = 0.0524

(c) If Luke is hit, there is a 60% chance that he'll live.

P(Luke survived when he got hit) = 0.60

P(Luke doesn't survived when he got hit) = 0.40

P(Luke survived when he doesn't get hit)= 1

P(Luke survived) = 0.60 * 0.20 + 1 * 0.8 = 0.92

so here

P(Luke was hit as it is given that he survived) = (0.6 * 0.2)/0.92 = 0.1304