Question 473251
This is a binomial distribution problem. Recall that the binomial pdf value is given by the formula


P(X = x) = (n C x)*(p^x)*(1-p)^(n-x)





In this case, n=30, p=1/5=0.2 and x=7.



So plug these values into the formula and evaluate



P(X = 7) = (30 C 7)*(0.2)^(7)*(1-0.2)^(30-7) 



P(X = 7) = (30 C 7)*(0.2)^(7)*(0.8)^(30-7) 



P(X = 7) = (2035800)*(0.2)^(7)*(0.8)^23 



Note: 30 C 7 = (30!)/(7!(30-7)!) = 2035800



P(X = 7) = (2035800)*(0.0000128)*(0.00590295810358705651712) 


 
P(X = 7) =  0.1538206989732163796166770688



P(X = 7) =  0.1538



Question: what is the probability that exactly 7 of them will visit disney world this year?


Answer: Probability is approximately 0.1538, which is roughly 15.38%