Gil, Nick and Sara are at target practice. Gil hits the target with 0.5 probability, Nick with 0.3 and Sara with 0.6, If they each take a shot, in that order

Question

Gil, Nick and Sara are at target practice. Gil hits the target with 0.5 probability, Nick with 0.3 and Sara with 0.6, If they each take a shot, in that order: What is the probability that they all hit the target? Probability that two of them hit the target? Probability that at least one?

Answer 1

1) Probability of all 3?

 

Since they are all independent events, you can just multiply the 3 probs together.

 

.5 * .3 * .6 

= .09

 

2) Probability of 2?

 

There's 3 different ways this can happen (using combinations, 3C2 = 3). So we need to prob of each outcome and then add all 3 together.

 

P(G & N hit, S misses) = .5 * .3 * .4 = .06

P(G & S hit, N misses) = .5 * .7 * .6 = .21

P(S & N hit, G misses) = .5 * .3 * .6 = .09

 

.21 + .09 + .06 = .36

 

3) Probability of at least one hitting?

 

The easiest way to do this is figure out 1 - P(nobody hits) because everything else would have to involve at least 1 person hitting.

 

P(they all miss) = .5 * .7 * .4 = .14

1 - .14 = .86