Chapter 13.5, Problem 6PPS

To determine

To determine whether the given events are independent or dependent, and find probability.

Answer to Problem 6PPS

The events are independent.

Probability is $\frac{3}{10}.$

Explanation of Solution

Given information:

In a game, you roll an even number on a die and then spin a spinner numbered 1 through 5 and get an odd number.

If any event A does not affect the outcome of an event B, then event A and B are independent whereas if it affects then the events are dependent.

Let us take event A= roll an even number on a die.

Even possibilities are {2,4,6}

Hence P(A) = $\frac{3}{6}=\frac{1}{2}$

Similarly let event B= spin a spinner numbered 1 through 5 and get an odd number.

Hence P(B) = $\frac{3}{5}$

Here we can determine that the events are independent. There is no affect of probability of rolling a die on spinning a spinner.

Therefore,

  $\begin{array}{l}P\left(A\text{ and }B\right)=P\left(A\right)\cdot P\left(B\right)\\ P\left(A\text{ and }B\right)=\frac{1}{2}\cdot \frac{3}{5}=\frac{3}{10}\end{array}$