Chapter 12.7, Problem 48HP

a.

To determine

Find the probability.

Answer to Problem 48HP

  $0.0031$

Explanation of Solution

Given information:

Multiple-choice test of $10$ question has four choices, $7$ question correct.

Calculation:

The probability that $7$ question correct,

  $\begin{array}{l}P\left(X=7\right)=\left(\underset{7}{\overset{10}{{\displaystyle }}}\right){\left(0.25\right)}^7{\left(0.75\right)}^{10-7}\\ =0.0031\end{array}$

Hence the probability is $0.0031$ .

b.

To determine

Find the probability.

Answer to Problem 48HP

  $0.0000286$

Explanation of Solution

Given information:

Multiple-choice test of $10$ question has four choices, $9$ question correct.

Calculation:

The probability that $9$ question correct,

  $\begin{array}{l}P\left(X=9\right)=\left(\underset{9}{\overset{10}{{\displaystyle }}}\right){\left(0.25\right)}^9{\left(0.75\right)}^{10-9}\\ =0.0000286\end{array}$

Hence the probability is $0.0000286$ .

c.

To determine

Find the probability.

Answer to Problem 48HP

  $0.0563$

Explanation of Solution

Given information:

Multiple-choice test of $10$ question has four choices, $0$ question correct.

Calculation:

The probability that $0$ question correct,

  $\begin{array}{l}P\left(X=0\right)=\left(\underset{0}{\overset{10}{{\displaystyle }}}\right){\left(0.25\right)}^0{\left(0.75\right)}^{10-0}\\ =0.0563\end{array}$

Hence the probability is $0.0563$ .

d.

To determine

Find the probability.

Answer to Problem 48HP

  $0.2503$

Explanation of Solution

Given information:

Multiple-choice test of $10$ question has four choices, $3$ question correct.

Calculation:

The probability that $3$ question correct,

  $\begin{array}{l}P\left(X=3\right)=\left(\underset{3}{\overset{10}{{\displaystyle }}}\right){\left(0.25\right)}^3{\left(0.75\right)}^{10-3}\\ =0.2503\end{array}$

Hence the probability is $0.2503$ .