Question

If a baseball player has a batting average of 0.420, what is the probability that the player will get at least 2 hits in the next four times at bat?

Answer 1

Binomial distribution. Do you know it?

Answer 2

No, can you help me solve this?

Answer 3

You've never even heard of binomial distribution?

Answer 4

Yes I've heard of it but It's not clear to me.

Answer 5

Well. To get \(k\) success with \(n\) tries and each try has probability \(p\), we say the probability is: \[
{n\choose k}p^k(1-p)^{n-k}
\]

Answer 6

Will will bat 4 times. His probability of hitting it is 0.420.
We want the probability he its it at least 2 times, meaning he hits it 2, 3, or 4 times.

Answer 7

Can you try to figure out which number goes where?

Answer 8

not really, I really don't get it..

Answer 9

0.42(1-0.42)^4-^2 This doesn't even look correct. Is there a format that I should know?

Answer 10

In this case, there are 4 tries, so \(n=4\).

Answer 11

So we have, so far \[
{4\choose k}p^k(1-p)^{4-k}
\]

Answer 12

The probability of success is given by batting average, so \(p=0.420\) and \(1-p=0.580\).
Now we have: \[
{4\choose k}(0.420)^k(0.580)^{4-k}
\]

Answer 13

At least two hits... that mean 2 hits, 3 hits, or 4 hits.

Answer 14

So then k is the # of hits then correct?

Answer 15

yes

Answer 16

Then I would replace the k with 2 to get the correct format?

Answer 17

no, you need to find probabilities for 2, 3, and 4. Then combine them.

Answer 18

okay