Chapter 10.2, Problem 28E

To determine

To justify: the two events are dependent or independent

Answer to Problem 28E

Conclude the events are not independent.

Explanation of Solution

Given:

  

Calculation:

Event A represent sum of outcomes which are greater than 2 but less than 9, and event B represent sum of outcomes which are greater than 5 and less than 9.

Two events A and B are independent if and only if the probability that both events occur is the product of the probabilities of the event. Symbolically,

  $P\left(A\text{ and }B\right)=P\left(A\right)\cdot P\left(B\right)\dots \left(1\right)$

Use the sample space and compute the following probabilities.

  $\begin{array}{l}P\left(A\right)=\frac{12}{36},P\left(B\right)=\frac{4}{36}\\ P\left(A\text{ and }B\right)=\frac{2}{36}\end{array}$

Substitute the values in rule (1). Since,

  $\frac{12}{36}\cdot \frac{4}{36}\ne \frac{2}{36}$

Conclude the events are not independent.

Conclusion:

Therefore, conclude the events are not independent.