The probability of rolling a number greater than 2 on a die is 2/3. Find the probability that on the next 7 rolls, exactly 3 show a number greater than 2?

Question

 Got this as a question for homework and have completely lost my mind trying to solve it.

Answer 1

This is a binomial distribution B(n,p) with parameters n = 7 and p = 2/3.  The probability of getting exactly k successes is given by 

 

P(X=k) = _nC_k*p^k*(1-p)^(n-k)  

 

_nC_k is the binomial coefficient = n!/(k!(n-k)!) 

 

Plug in 3 for k and solve.