Chapter 5.2, Problem 42E

Flawed parts: On a certain day, a foundry manufactured 500 cast aluminum parts. Some of these had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents tile results.

Find the probability that a randomly chosen part has a major flaw.

Find the probability that a randomly chosen part has a minor flaw.

Find the probability that a randomly chosen part has a flaw (major or minor).

Find the probability that a randomly chosen part has no major flaw.

Find the probability that a randomly chosen part has no flaw.

To determine

To find: The probability of a randomly chosen part has a major flaw.

Answer to Problem 42E

The probability of a randomly chosen part has a major flaw is $0.11$

Explanation of Solution

Given information: The number of cast aluminum parts a foundry manufacturedis $500$ . The table is shown below.

  $\boxed{\begin{array}{ccc}\begin{array}{c}\\ \text{Major Flaw}\\ \text{No Major Flaw}\end{array}& \begin{array}{c}\text{Minor Flaw}\\ 20\\ 75\end{array}& \begin{array}{c}\text{No Minor Flaw}\\ 35\\ 370\end{array}\end{array}}$

Calculation:

The number of chosen parts has a major flaw is,

  $20+30=55$

Therefore,

  $\begin{array}{l}P(\text{Major Flaw})=\frac{55}{500}\\ =0.11\end{array}$

To determine

To find: The probability of a randomly chosen part has a minor flaw.

Answer to Problem 42E

The probability of a randomly chosen part has a minor flaw is $0.19$

Explanation of Solution

Given information: The number of cast aluminum parts a foundry manufacturedis $500$ . The table is shown below.

  $\boxed{\begin{array}{ccc}\begin{array}{c}\\ \text{Major Flaw}\\ \text{No Major Flaw}\end{array}& \begin{array}{c}\text{Minor Flaw}\\ 20\\ 75\end{array}& \begin{array}{c}\text{No Minor Flaw}\\ 35\\ 370\end{array}\end{array}}$

Calculation:

The number of chosen parts has a minor flaw is,

  $20+75=95$

So,

  $\begin{array}{l}P(\text{Minor Flaw})=\frac{95}{500}\\ =0.19\end{array}$

To determine

To find: The probability of a randomly chosen part has a flaw $(\text{major or minor})$ .

Answer to Problem 42E

The probability of a randomly chosen part has a flaw $(\text{major or minor})$ is $0.26$

Explanation of Solution

Given information: The number of cast aluminum parts a foundry manufacturedis $500$ . The table is shown below.

  $\boxed{\begin{array}{ccc}\begin{array}{c}\\ \text{Major Flaw}\\ \text{No Major Flaw}\end{array}& \begin{array}{c}\text{Minor Flaw}\\ 20\\ 75\end{array}& \begin{array}{c}\text{No Minor Flaw}\\ 35\\ 370\end{array}\end{array}}$

Calculation:

The number of chosen parts has a flaw is,

  $20+35+75=130$

Therefore,

  $\begin{array}{l}P(\text{Has a flaw})=\frac{130}{500}\\ =0.26\end{array}$

To determine

To find: The probability of a randomly chosen part has no major flaw.

Answer to Problem 42E

The probability of a randomly chosen part has no major flaw is $0.89$

Explanation of Solution

Given information: The number of cast aluminum parts a foundry manufacturedis $500$ . The table is shown below.

  $\boxed{\begin{array}{ccc}\begin{array}{c}\\ \text{Major Flaw}\\ \text{No Major Flaw}\end{array}& \begin{array}{c}\text{Minor Flaw}\\ 20\\ 75\end{array}& \begin{array}{c}\text{No Minor Flaw}\\ 35\\ 370\end{array}\end{array}}$

Calculation:

The number of chosen parts has no major flaw is,

  $75+370=445$

Hence,

  $P(\text{No major flaw})=\frac{445}{500}=0.89$

To determine

To find: The probability of a randomly chosen part has no flaw.

Answer to Problem 42E

The probability of a randomly chosen part has no flaw is $0.74$

Explanation of Solution

Given information: The number of cast aluminum parts a foundry manufacturedis $500$ . The table is shown below.

  $\boxed{\begin{array}{ccc}\begin{array}{c}\\ \text{Major Flaw}\\ \text{No Major Flaw}\end{array}& \begin{array}{c}\text{Minor Flaw}\\ 20\\ 75\end{array}& \begin{array}{c}\text{No Minor Flaw}\\ 35\\ 370\end{array}\end{array}}$

Calculation:

The number of chosen parts has no flawis $370$ .

Therefore,

  $P(\text{No flaw}\text{})=\frac{370}{500}=0.74$