if i had an 8 sided die and I rolled it 13 times what would be the probability of rolling exactly 5 prime numbers

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Eight sided die has sapmle space S={ 1,2,3,4,5,6,7,8}
E= Event getting prime of face of die ={2,3,5,7}
P(E)= n(E)/n(S)= 4/8=1/2
P(not E) =1-(1/2)=1/2
Probabilty getting E exactly 5 times in rolling of 13 times.
P( E,r=5)=C(13,5)(1/2)^5(1/2)^(13-5)
(by binomial distribution)
P(E)=C(13,5)(1/2)^13

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