Chapter 8.6, Problem 67E

(a)

To determine

To find: the probability that a sale will be made with all six contacts.

Answer to Problem 67E

The probability that a sale will be made with all six contacts is $\frac{1}{15625}$ .

Explanation of Solution

Given information:

A sales representative makes sales on approximately one fifth of all calls. On a given day, the representative contacts six potential clients.

Calculation:

Given that probability of sales representative makes sales on approximately is

  $p\left(A\right)=\frac{1}{5}$

Probability of sales representative makes second sales on approximately is $p\left(A\right)=\frac{1}{5}$ , and so on. Because these events are independent, you can conclude that a probability that a sale will be made with all six contacts is

  $\begin{array}{c}{\left[p\left(A\right)\right]}^6={\left(\frac{1}{5}\right)}^6\\ =\frac{1}{15625}\end{array}$

(a)

To determine

To find: the probability that a sale will be made with all six contacts.

Answer to Problem 67E

The probability that a sale will be made with all six contacts is $\frac{1}{15625}$ .

Explanation of Solution

Given information:

A sales representative makes sales on approximately one fifth of all calls. On a given day, the representative contacts six potential clients.

Calculation:

Given that probability of sales representative makes sales on approximately is

  $p\left(A\right)=\frac{1}{5}$

Probability of sales representative makes second sales on approximately is $p\left(A\right)=\frac{1}{5}$ , and so on. Because these events are independent, you can conclude that a probability that a sale will be made with all six contacts is

  $\begin{array}{c}{\left[p\left(A\right)\right]}^6={\left(\frac{1}{5}\right)}^6\\ =\frac{1}{15625}\end{array}$

(b)

To determine

To find: the probability that a sale will be made with none of the contacts.

Answer to Problem 67E

The probability that a sale will be made with none of the contacts is $\frac{4096}{15625}$ .

Explanation of Solution

Given information:

A sales representative makes sales on approximately one fifth of all calls. On a given day, the representative contacts six potential clients.

Calculation:

Given that probability of sales representative makes sales on approximately is

  $p\left(A\right)=\frac{1}{5}$

Probability of sales representative doesn’t makes ales on approximately is,

  $\begin{array}{c}p\left(B\right)=1-p\left(A\right)\\ =1-\frac{1}{5}\\ =\frac{4}{5}\end{array}$

Probability of sales representative doesn’t make sales on approximately is $p\left(B\right)=\frac{4}{5}$ , and so on. Because these events are independent, you can conclude that the probability that a sale will not made all six contacts is

  $\begin{array}{c}{\left[p\left(B\right)\right]}^6={\left(\frac{4}{5}\right)}^6\\ =\frac{4096}{15625}\end{array}$

(c)

To determine

To find: the probability that a sale will be made with at least one contact.

Answer to Problem 67E

The probability that a sale will be made with at least one contact is $\frac{11529}{15625}$ .

Explanation of Solution

Given information:

A sales representative makes sales on approximately one fifth of all calls. On a given day, the representative contacts six potential clients.

Calculation:

The probability that a sale will be made with a least one contact

  $\begin{array}{l}=1-\text{none}\text{of}\text{these}\\ \text{=1-}\frac{4096}{15625}\\ =\frac{11529}{15625}\end{array}$

The probability that a sale will be made with at least one contact is $\frac{11529}{15625}$ .