Chapter 13.5, Problem 42E

a.

To determine

To calculate: The probability that a defective chip is selected.

Answer to Problem 42E

The probability that a defective chip is selected is $\frac{33}{500}$ .

Explanation of Solution

Given information:

A table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Formula used:

Probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Calculation:

Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Total number of chips manufactured are 1000 and number of defective chips are 66.

Let A be an event that chip is defected.

Recall that probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Probability that defected chip is randomly selected is,

  $\begin{array}{c}P\left(A\right)=\frac{66}{1000}\\ =\frac{33}{500}\end{array}$

Thus, the probability that a defective chip is selected is $\frac{33}{500}$ .

b.

To determine

To calculate: The probability that defective chip came from 3-D Images Inc.

Answer to Problem 42E

The probability that defective chip came from 3-D Images Inc. is $\frac{7}{22}$ .

Explanation of Solution

Given information:

A table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Formula used:

Probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Given an event Q, the conditional probability of event A is

  $P\left(A|Q\right)=\frac{P\left(A\text{ and Q}\right)}{P\left(Q\right)}$ where $P\left(Q\right)\ne 0$ .

Calculation:

Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Total number of chips manufactured are 1000 and number of defective chips are 66.

Let A be an event that chip is from 3-D Images Inc. and B be an event that chip is defected.

Recall that probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Probability that chip is defected,

  $P\left(B\right)=\frac{66}{1000}$

Probability that chip is from 3-D Images Inc. and chip is defected.

  $P\left(A\text{ and B}\right)=\frac{21}{1000}$

Recall that given an event Q, the conditional probability of event A is $P\left(A|Q\right)=\frac{P\left(A\text{ and Q}\right)}{P\left(Q\right)}$ where $P\left(Q\right)\ne 0$ .

The probability that defective chip came from 3-D Images Inc.

  $\begin{array}{c}P\left(A|B\right)=\frac{\frac{21}{1000}}{\frac{66}{1000}}\\ =\frac{21}{66}\\ =\frac{7}{22}\end{array}$

Thus, the probability that defective chip came from 3-D Images Inc. is $\frac{7}{22}$ .

c.

To determine

To calculate: The probability that a functional chip is selected.

Answer to Problem 42E

The probability that a functional chip is selected is $\frac{457}{500}$ .

Explanation of Solution

Given information:

A table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Formula used:

Probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Calculation:

Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Total number of chips manufactured are 1000, number of functional chips are 934 and number of defective chips are 66.

Let A be an event that chip is functional.

Recall that probability of an event E is $P\left(\text{E}\right)=\frac{\text{number of outcome}}{\text{total number of outcome}}$ .

Probability that functional chip is randomly selected is,

  $\begin{array}{c}P\left(A\right)=\frac{934}{1000}\\ =\frac{457}{500}\end{array}$

Thus, the probability that a functional chip is selected is $\frac{457}{500}$ .

d.

To determine

To explain: The company that produce most reliable graphic chip.

Answer to Problem 42E

The company that produce most reliable graphic chip is CyberChip Corp.

Explanation of Solution

Given information:

A table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Consider the provided information that a table that depicts number of defective and functioning chips manufactured by 3 companies.

$\begin{array}{ccc}\text{Company}& \begin{array}{c}\text{Number of}\\ \text{functioning chips}\end{array}& \begin{array}{c}\text{Number of}\\ \text{defective chips}\end{array}\\ \text{CyberChip Corp}\text{.}& 475& 25\\ 3-\text{D images, Inc}\text{.}& 279& 21\\ \text{MegaView Designs}& 180& 20\end{array}$

Total number of chips manufactured are 1000, number of functional chips are 934 and number of defective chips are 66.

Compute the ratio of defective to functioning chip for each company.

For CyberChip Corp. the ratio of defective to functioning chip is,

$\frac{25}{475}\times 100\%=5.26\%$

For 3-D Images Inc. the ratio of defective to functioning chip is,

$\frac{21}{279}\times 100\%=7.53\%$

For MegaView Designs the ratio of defective to functioning chip is,

$\frac{20}{180}\times 100\%=11.11\%$

Observe that least defective to functioning chip ratio is for CyberChip Corp. so it is the most reliable company to manufacture graphic chip.

Thus, the company that produce most reliable graphic chip is CyberChip Corp.