Find the probability of having 2,3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40%.

0.45033504848

The binomial formula is given by
nCk⋅ρk(1−ρ)n−k thus the result for x would be

p(x=2)=(5!(5−2!)2!)(.4)2(1−.4)5−2=0.3456

p(x=3)=(5!(5−3!)3!)(.4)3(1−.4)5−3=0.13824

p(x=4)=(5!(5−4!)4!)(.4)4(1−.4)5−4=0.027648

p(a∪b∪c)=p(a)+p(b)+p(c)−p(a)⋅p(b)−p(a)⋅p(c)−p(b)⋅p(c)=.3456+.13824+.027648−.047775744−.0095551488−0.00382205952

p(a∪b∪c)=0.45033504848

0.02040816326