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

Maria's batting average = 5/13 = .385

Maggie's is 4/7 = .571

Chung's is 5/11 = .455

choose Maggie 571>455>385

team's weighted average is (5+4+5)/(13+7+11) = 14/31 = .452 where the average gives greater weight to the batters with more at bats

4/7 + 5/11 + 5/13

add them by converting each fraction to a common denominator = 7(11)(13)

then divide by 3

= (572+455+385)/1001 = 1412/1001= 1.4106 divided by 3 = .470

(385+455 + 571)/3 = .470 = the average weighting each batter's average with equal weights,