Chapter 6.3, Problem 78E

To determine

To calculate; the value of $P(X\ge 3)$ .

Answer to Problem 78E

  $P(X\ge 3)=0.0116=1.16\%$

Explanation of Solution

Given;

  $\begin{array}{l}n=10\\ p=0.05\end{array}$

Explanation;

  $\begin{array}{l}\text{Definition Binomial Probability:}\\ $ \text{P(X = k) = }\left(\begin{array}{l}n\\ k\end{array}\right)\times p^k\times {(1-p)}^{n-k}$\end{array}$

  $\begin{array}{}$ \text{P(X = 0) = }\left(\begin{array}{l}10\\ 0\end{array}\right)\times {(0.05)}^0\times {(0.95)}^{10-0}\approx 0.5987$$ \text{P(X = 1) = }\left(\begin{array}{l}10\\ 1\end{array}\right)\times {(0.05)}^1\times {(0.95)}^{10-1}\approx 0.3151$$ \text{P(X = 2) = }\left(\begin{array}{l}10\\ 2\end{array}\right)\times {(0.05)}^2\times {(0.95)}^{10-2}\approx 0.0746$\end{array}$

  $P(X\ge 3)=1-P(X=0)-P(X=1)-P(X=2)=1-0.5987-0.3151-0.0746=0.0116=1.16\%$