Chapter 6.3, Problem 82E

To determine

To find: The $P\left(Y=4\right)$ and interpret it.

Answer to Problem 82E

The probability is 0.0984.

Explanation of Solution

Given:

Number of trials ( n ) = 6

Probability of success ( p ) = 0.90

Formula used:

The formula to compute the binomial probability is:

  $P\left(X=r\right){=}^n{C}_r\times p^r\times {\left(1-p\right)}^{n-r}$

Here.

  $\begin{array}{l}r\text{ is the number of successes}\\ n\text{ is the number of trials}\\ p\text{ is the probability of success}\end{array}$

Calculation:

Consider, Y be the random variable that follows the binomial distribution with n = 6 and p = 0.90.

  $P\left(Y=4\right)$ can be calculated as:

  $\begin{array}{c}P\left(Y=4\right){=}^6{C}_4\times {\left(0.90\right)}^4\times {\left(1-0.90\right)}^{6-4}\\ =0.0984\end{array}$

Thus, the required probability is 0.0984.

Interpretation:

The probability of 4 out of 7 trains that arrive late on chosen days is 9.84%