A fair die is rolled 10 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times?

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Answer 1 · 2018-07-26T00:44:32

#375/1024~~0.366#

We can solve this using a binomial probability. The relationship I like to start with is:

#sum_(k=0)^(n)C_(n,k)(p)^k(1-p)^(n-k)=1#

In our case, we have 10 rolls, so #n=10#.

The probability of rolling even is #1/2#, so #p=1/2#.

We're interested in #2 <=k <= 4#.

#C_(10,2)(1/2)^2(1/2)^(8)+C_(10,3)(1/2)^3(1/2)^(7)+C_(10,4)(1/2)^4(1/2)^(6)#

#45xx(1/1024)+120xx(1/1024)+210xx(1/1024)#

#375/1024~~0.366#