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The probability of 3 red cars in a parking lot with 16 cars is 10%. What is the...

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lxsptter | Student, Undergraduate | (Level 2) Valedictorian

Posted January 20, 2012 at 2:09 PM via web

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The probability of 3 red cars in a parking lot with 16 cars is 10%. What is the probability that in a random group of 5 cars one is red.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 20, 2012 at 3:15 PM (Answer #1)

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The probability of 3 red cars in a parking lot with 16 cars is 10%. The number of ways of picking 5 cars of the 16 is given by ``16C5. Of these, the number of ways of picking only 1 red car is 13C4*3C1, the number of ways of picking 2 red cars is 13C3*3C2 and the number of ways of picking 3 red cars is 13C2*3C3

The probability that one car is red in the group of 5 cars that is picked is:` (13C4*3C1 + 13C3*3C2 + 13C2*3C3)/(16C5) ~~ 0.7053` .

Multiplying this with the probability that the number of red cars in the 16 cars at the parking lot is 10%, the final probability is 0.07053.

The probability of a random group of cars having 1 red car that are picked from the parking lot is 0.07053.

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