wildmango one year ago 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?

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1. wio

Binomial distribution. Do you know it?

2. wildmango

No, can you help me solve this?

3. wio

You've never even heard of binomial distribution?

4. wildmango

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

5. wio

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

6. wio

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.

7. wio

Can you try to figure out which number goes where?

8. wildmango

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

9. wildmango

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

10. wio

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

11. wio

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

12. wio

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

13. wio

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

14. wildmango

So then k is the # of hits then correct?

15. wio

yes

16. wildmango

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

17. wio

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

18. wildmango

okay