# 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%?

Jul 17, 2016

0.45033504848

#### Explanation:

The binomial formula is given by
$n C k \cdot {\rho}^{k} {\left(1 - \rho\right)}^{n - k}$ 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

$p \left(a \cup b \cup c\right) = p \left(a\right) + p \left(b\right) + p \left(c\right) - p \left(a\right) \cdot p \left(b\right) - p \left(a\right) \cdot p \left(c\right) - p \left(b\right) \cdot p \left(c\right) = .3456 + .13824 + .027648 - .047775744 - .0095551488 - 0.00382205952$

$p \left(a \cup b \cup c\right) = 0.45033504848$