A baseball player has had 14 hits in 60 times at bat in the last 20 games. How many hits does the batter need in her next ten at bats to increase the probability of her getting a hit to 0.300?
The number of games is irrelevant. Starting now, we have 14/60 = .23333
Now, if she goes to bat 10 more times, and gets x hits, we want (14+x)/(60+10) = .300
14+x = .300 * 70 = 21
SO, if she hits 7/10, her avg will rise to .300
To determine how many hits the batter needs in her next ten at-bats to increase her probability of getting a hit to 0.300, we have to calculate the number of hits she already has and the number of at-bats she already made.
In the last 20 games, the batter had 14 hits in 60 at-bats. To find the current probability of the batter getting a hit in one at-bat, we divide the number of hits by the number of at-bats:
Probability = Number of hits / Number of at-bats
Probability = 14 / 60 ≈ 0.233
Therefore, the current probability of the batter getting a hit in one at-bat is approximately 0.233.
To increase this probability to 0.300, we can set up the following equation:
(New number of hits + 14) / (New number of at-bats + 60) = 0.300
Simplifying this equation, we get:
New number of hits + 14 = 0.300 * (New number of at-bats + 60)
New number of hits + 14 = 0.300 * New number of at-bats + 18
New number of hits = 0.300 * New number of at-bats + 4
We know that the new number of at-bats will be 10 since the batter will have 10 more at-bats. Substituting this value, we can solve for the new number of hits:
New number of hits = 0.300 * 10 + 4
New number of hits = 3 + 4
New number of hits = 7
Therefore, the batter needs to make 7 hits in her next 10 at-bats to increase her probability of getting a hit to 0.300.