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Ben rolls four fair 10-sided dice. What is the probability that exactly two of the dice show a prime number?

 Apr 14, 2016
 #1
avatar+129852 
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The chance that any die shows a prime number = 4/10......so we have

 

C(4,2) * (.4)^2 * (.6)^2   =   28/45  = about 62.22%

 

 

cool cool cool

 Apr 14, 2016
 #2
avatar+561 
+3

I don't think that is the correct answer(I Think)

The probability that a 10-sided die rolls a prime number is (4/10) = (2/5)  since the primes it can roll are 2, 3, 5, and 7. We can choose which dice show a prime number in 4C2 = 6 ways. Then, there is a  chance that the chosen dice will actually roll a prime number and the other dice won't. Therefore, the total probability that exactly two dice show a prime number is 6 * 36/625 = 216/625 .

Art of Problem Solving Solution @above

My solution:

Do what CPhill did, C(4,2) * (.4)^2 * (.6)^2 = 216/625.

 Dec 21, 2016

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