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wildmango
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?
Binomial distribution. Do you know it?
No, can you help me solve this?
You've never even heard of binomial distribution?
Yes I've heard of it but It's not clear to me.
Well. To get \(k\) success with \(n\) tries and each try has probability \(p\), we say the probability is: \[ {n\choose k}p^k(1-p)^{n-k} \]
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.
Can you try to figure out which number goes where?
not really, I really don't get it..
0.42(1-0.42)^4-^2 This doesn't even look correct. Is there a format that I should know?
In this case, there are 4 tries, so \(n=4\).
So we have, so far \[ {4\choose k}p^k(1-p)^{4-k} \]
The probability of success is given by batting average, so \(p=0.420\) and \(1-p=0.580\). Now we have: \[ {4\choose k}(0.420)^k(0.580)^{4-k} \]
At least two hits... that mean 2 hits, 3 hits, or 4 hits.
So then k is the # of hits then correct?
Then I would replace the k with 2 to get the correct format?
no, you need to find probabilities for 2, 3, and 4. Then combine them.