Chapter 3, Problem 3.94LM

Which of the following pairs of events are mutually exclusive? Justify your response.

1. a. {The Dow Jones Industrial Average increases on Monday.}, {A large New York bank decreases its prime interest rate on Monday.}
2. b. {The next sale by a PC retailer is a notebook computer}, {The next sale by a PC retailer is a desktop computer.}
3. c. {You reinvest all your dividend income in a limited partnership.}, {You reinvest all your dividend income in a money market fund.}

To determine

To verify: Whether the pair of events are mutually exclusive or not and to justify the reason.

Answer to Problem 3.94LM

The events are not mutually exclusive.

Explanation of Solution

Given info:

The pairs of events are,

$\left\{\begin{array}{l}\text{The Dow Jones Industrial }\\ \text{average increases on monday}\end{array}\right\}\left\{\begin{array}{l}\text{A Large New york bank decreases }\\ \text{its prime intrest rate on monday}\end{array}\right\}$

Calculation:

Two events A and B are mutually exclusive if A and B have no sample points in common. That is, $P\left(A\cap B\right)=0$.

For the pairs of events is,

$\left\{\begin{array}{l}\text{The Dow Jones Industrial }\\ \text{average increases on monday}\end{array}\right\}\left\{\begin{array}{l}\text{A Large New york bank decreases }\\ \text{its prime intrest rate on monday}\end{array}\right\}$

The events are not mutually exclusive since they could occur simultaneously and have sample points in common.

To determine

To verify: Whether the pair of events are mutually exclusive or not and to justify the reason.

Answer to Problem 3.94LM

The events are mutually exclusive.

Explanation of Solution

Given info:

The pairs of events are,

$\left\{\begin{array}{l}\text{The next sale by a PC retailer }\\ \text{is a notebook computer }\end{array}\right\}\left\{\begin{array}{l}\text{The next sale by a PC retailer }\\ \text{is a desktop computer }\end{array}\right\}$

Calculation:

For the pairs of events is,

$\left\{\begin{array}{l}\text{The next sale by a PC retailer }\\ \text{is a notebook computer }\end{array}\right\}\left\{\begin{array}{l}\text{The next sale by a PC retailer }\\ \text{is a desktop computer }\end{array}\right\}$

The events are mutually exclusive since they could not occur simultaneously. That is, the next sale by a PC retailer could not be both a notebook and a desktop computer.

To determine

To verify: Whether the pair of events are mutually exclusive or not and to justify the reason.

Answer to Problem 3.94LM

The events are mutually exclusive.

Explanation of Solution

Given info:

The pairs of events are,

$\left\{\begin{array}{l}\text{You}\text{reinvest}\text{all}\text{your}\text{dividend}\text{income}\\ \text{in}\text{a}\text{limited}\text{partnership}\end{array}\right\}\left\{\begin{array}{l}\text{You}\text{reinvest}\text{all}\text{your}\text{dividend}\text{income}\\ \text{in}\text{a}\text{money}\text{market}\text{fund}\end{array}\right\}$

Calculation:

For the pairs of events is,

$\left\{\begin{array}{l}\text{You}\text{reinvest}\text{all}\text{your}\text{dividend}\text{income}\\ \text{in}\text{a}\text{limited}\text{partnership}\end{array}\right\}\left\{\begin{array}{l}\text{You}\text{reinvest}\text{all}\text{your}\text{dividend}\text{income}\\ \text{in}\text{a}\text{money}\text{market}\text{fund}\end{array}\right\}$

The events are mutually exclusive since they could not occur simultaneously.