Question 341102: Of the 16 students at a party, 4 are from Colorado, 5 are from Utah, and 7 are from Ohio. Four students are selected at random from this group of 16 students. Find the following probablities:
a. All four of the students are from Ohio.
b. None of the students are from Utah.
c. At least one of the students is from Utah.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Of the 16 students at a party, 4 are from Colorado, 5 are from Utah, and 7 are from Ohio. Four students are selected at random from this group of 16 students. Find the following probablities:
a. All four of the students are from Ohio.
# of ways to pick 4 from 7: 7C4 = (7*6*5*4)/(1*2*3*4) = 35
# of ways to randomly pick 4 from 16 = 16C4 = (16*15*14*13)(1*2*3*4) = 1820
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P(pick 4 from Ohio) = 35/1820 = 0.0192
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b. None of the students are from Utah.
P(none from Utah) = 11C4/16C4 = 330/1820 =0.1813
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c. At least one of the students is from Utah.
P(at least one from U) = 1 - P(none from U)
= 1 - 0.1813
= 0.8187
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Cheers,
Stan H.
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