Question

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

Answer 1

0.45033504848

Explanation:

The binomial formula is given by
`nCk * rho^k(1- rho)^(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 uu b uu 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 uu b uu c) = 0.45033504848`