Chapter 10, Problem 8CA

(a)

To determine

To calculate:

The probability when all the three mowers are unusable on a particular given day.

Answer to Problem 8CA

The probability when all the three mowers are unusable on a particular given day is $0.0014$ .

Explanation of Solution

Given information:

Because one of the mowers is $10\%$ unusable, one is $8\%$ unusable and another $18\%$ of the time is unusable.

i.e.

  $\begin{array}{l}P(Mower1isunusable)=10\%\\ P(Mower1isunusable)=0.10\end{array}$

  $\begin{array}{l}P(Mower2isunusable)=8\%\\ P(Mower2isunusable)=0.08\end{array}$

  $\begin{array}{l}P(Mower3isunusable)=18\%\\ P(Mower3isunusable)=0.18\end{array}$

Calculation:

The probability when all the three mowers are unusable on a particular given day can be found out as:

  $P(all3mowersunusable)=P(Mower1isunusable)\times P(Mower2isunusable)\times P(Mower3isunusable)$

Substitute the values,

  $\begin{array}{l}P(all3mowersunusable)=0.10\times 0.08\times 0.18\\ P(all3mowersunusable)=1.44\times {10}^{-3}\\ P(all3mowersunusable)=0.0014\end{array}$

Thus, the probability when all the three mowers are unusable on a particular given day is $0.0014$ .

(b)

To determine

To calculate:

The probability when at least one of the mowers is unusable on a particular given day.

Answer to Problem 8CA

The probability when at least one of the mowers is unusable on a particular given day is $0.9986$

Explanation of Solution

Given information:

Because one of the mowers is $10\%$ unusable, one is $8\%$ unusable and another $18\%$ of the time is unusable.

i.e.

  $\begin{array}{l}P(Mower1isunusable)=10\%\\ P(Mower1isunusable)=0.10\end{array}$

  $\begin{array}{l}P(Mower2isunusable)=8\%\\ P(Mower2isunusable)=0.08\end{array}$

  $\begin{array}{l}P(Mower3isunusable)=18\%\\ P(Mower3isunusable)=0.18\end{array}$

Calculation:

The probability when at least one of the mowers is unusable on a particular given day can be found out as:

  $P(Atleast1mowerisunusable)=1-P(all3mowersunusable)$

Substitute the values,

  $\begin{array}{l}P(Atleast1mowerisunusable)=1-0.0014\\ P(Atleast1mowerisunusable)=0.9986\end{array}$

Thus, the probability when at least one of the mowers is unusable on a particular given day is $0.9986$ .

(c)

To determine

To explain:

The probability affecting the productivity of lawn-moving business on a given day.

Answer to Problem 8CA

If the least reliable mower stops working completely, it wouldn’t affect the productivity of lawn-moving business on a given day.

Explanation of Solution

It is said the owner can stay productive for as long as one of the mowers is working. So, if the least reliable mower stops working completely, it wouldn’t affect productivity of lawn-moving business on a given day.