ratio and probability question

Question

Imagine you are the coach for a co-ed softball championship game. There are two players on base and two outs. You are about to name a pinch hitter among three players. Maggie has gotten hits 4 out of her last 7 times at bat. Chung has gotten hits 5 out of his last 11 times at bat and Maria's ratio of hits to non-hits is 5 to 8.

a. What is Maria's batting average to the nearest thousandth?

b. At these rates, which player should you choose?

c. If you consider Maggie, Chung, and Maria as a team, what's that team's batting average (assuming that Maria had 13 times at bat)? Note how this is different than finding the average of their batting averages.

Answer 1

a 5/13 = 0.385 batting average for Maria

b. Maggie is 4 out 7 which is 4/7 = a 0.571 batting average

Chung is 5 out of 11 which is 5/11 = 0.454 batting average

Maggie wins. Pick her for designated batter. .571>.454>.385

c. 5/11, 4/7, 5/13 averages to = .470 batting average, but that weighs each equally.

a weighted average would weigh each according to how many at bats each had

total at bats = 7+11+13 =31

total hits = 4+5+5 = 14

14/31 = 0.452= the team batting average