Question 190311: A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions.
If he bats 5 times in a game, what is the probability he will hit exactly one home run?
If he comes to bat 5 times, what is the probability he will hit at least one home run?
If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit?
thanks for your help
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions.
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If he bats 5 times in a game, what is the probability he will hit exactly one home run?
It's binomial with n=5, p = 1/12, x = 1
If you use a TI calculator you get binompdf(5,12^-1,1) = 0.2942
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If you do not have a TI: P(x=1) = 5C1(1/12)^1(11/12)^4
= 5*(1/12)(0.70607) = 0.2942
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If he comes to bat 5 times, what is the probability he will hit at least one home run?
P(at least one) = 1 - P(no home runs) = 1-binompdf(5,12^-1,0) = 0.3528
OR
P(at least one) = 1-P(no home runs) = 1 - 5C0(1/12)^0(11/12)^5
= 1 - 1*1* = 1-0.6472 = 0.3528
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If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit?
E(x) = np = 5(1/12) = 5/12
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Cheers,
Stan H.
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