Chapter 10.6, Problem 15E

To determine

To calculate:

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

Answer to Problem 15E

The error of probability calculation of six sided die is $0.161$ . The correct value is $0.032$ .

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 the resulted value is $P\left(k=3\right)\approx 0.161$ . This is the calculation error. So, need to calculate the correct probability value. Use the following calculation:

Consider the probability distribution formula:

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

  $P$ : Probability of success.

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 $0.032$