Question

Find the probability of exactly 3 successes p = 0.6, n = 5

Answer 1

0.3456 = 34.56%

Explanation:

Binomial distribution

`\displaystyle P(X=x)=\binom{n}{x} \cdot p^x \cdot (1-p)^(n-x)`

where:

• n = number of trials
• p = probability of success

Given:

• p = 0.6
• n = 5
• x = 3

Substitute the given values into the formula:

`\begin{aligned}\implies \displaystyle P(X=3) & =\binom{5}{3} \cdot 0.6^3 \cdot (1-0.6)^(5-3)\\ & = (5!)/(3!(5-3)!)\cdot 0.6^3 \cdot 0.4^2\\ & = 10 \cdot 0.216 \cdot 0.16\\ & =0.3456\end{aligned}`

Therefore, the probability of exactly 3 successes is 0.3456 = 34.56%