What statistics formula would apply in the following situation:

Question

An archer shoots arrows at a target, at either 40 yards (80% of the time) or at 60 yards (20%) and either right-handed (60% of the time) or left-handed (40%). After thousands of trials, her overall probablility hitting the bulls-eye is 25%, but her probability of a bulls-eye at 40 yards is 40% and her probability of a bulls-eye shooting right-handed is 30%. What statistics formula would let one determine the probability of her shooting a bulls-eye given the following:

Shooting at 40 yards right-handed.

Shooting at 40 yards left-handed.

Shooting at 60 yards right-handed.

Shooting at 60 yards left-handed.

The formula should be general so that more than 2 distinguishing criteria could be specified, for instance adding whether or not the wind was greater than 10 mph.

Answer 1

40 yds right handed is 30%

40 yds left handed is 50%

as (L+R)/2 = 40% (L+30)/2 = 40