Example 1:

In 530 at bats, a baseball player has a batting average of 0.241. In the next game, he has 4 at bats. What is the most likely number of hits he will get? Suppose he hits 3 of those swings. What is his new batting average to three places?

Most likely number of hits: New batting average:

Part 1: Most likely number of hits
The baseball player has a batting average of 0.241 after 530 at bats. This means that he has a 24.1% chance of getting a hit whenever he swings at a ball.

1. The most likely number of hits is the number of hits × batting average.
   So for the next 4 hits, the most likely number of hits is 4 × 0.241 = 0.964

2. We then round to the nearest whole number of hits.
   0.964 hits rounds to 1 hit

Part 2: New batting average

Batting average =

We calculate the new batting average using the fact that after his 530 at bats, the baseball player made 3 more hits from 4 more swings.

New batting average = =

Original number of hits = original batting average × original number of swings   = 0.241 × 530   = 127.73 which rounds to 128

New batting average =   =   = 0.245

Most likely number of hits:
New batting average: