Chapter 10.6, Problem 16E

To determine

To calculate:

The error of probability calculation of six sided die and resolves it

Answer to Problem 16E

The error of the problem is the missing of term $C{}_3$ . The correct probability value is

Explanation of Solution

Given information:

  

Formula used:

Probability distribution is given by the following expression:

  $P\left(ksuccesses\right)=C{}_k{p}^k{\left(1-p\right)}^{n-k}$

Where,

  $P$ : Probability of success.

Calculation:

In the given probability calculation, there is no use the correct formula which gives the wrong probability value $P\left(k=3\right)\approx 0.003$ .

The missing terms in the given calculation is $C{}_3$ is the error of the problem.

This is the calculation error. So, need to calculate the correct probability value. Use the following calculation:

Consider the probability distribution formula:

  $P\left(ksuccesses\right)=C{}_k{p}^k{\left(1-p\right)}^{n-k}\cdot \cdot \cdot \left(1\right)$

Put the values of $n=5,k=3,p=0.167$ in equation:

  $\begin{array}{l}P\left(k=3\right)=C{}_3{\left(0.167\right)}^3{\left(0.833\right)}^2\\ P\left(k=3\right)=0.032\end{array}$

The error of probability calculation of six sided die is resolved and the correct value is $0.032$