Question

A man shoots with a bow. There is a 70% chance that he hits with the first shot. If he hits, he gets more confidence, and then there is an 80% chance that he hits with other shots. If he misses with the first shot, his confidence drops, and then there is only a 60% chance that he hits with other shots. Per shoots 2 arrows. Find the probability that he gets 2 hits, 1 hit and no hits.

Answer 1

2 hits: 56%

1 hit : 32%

0 hits: 12%

Explanation:

2 hits: 0.7 * 0.8

1 hit : (.7*.2 + .3*.6) - .7*.8

0 hits: .3 * .4