Chapter 13.5, Problem 8PPS

To determine

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

Answer to Problem 8PPS

The events are dependent.

Probability is $\frac{2}{7}.$

Explanation of Solution

Given information:

There are 3 green and 4 blue marbles.

First blue is drawn. Then second blue marble is drawn.

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.

Here we can determine that the events are dependent. As there is no replacement probability of first event affects the probability of second event.

Let us take event A= blue marble is drawn

Hence P(A) = $\frac{4}{7}$

Similarly let event B= second blue marble is drawn from the remaining 6 marbles.

One blue marble is already taken,

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

Therefore,

  $P\left(A\text{ and }B\right)=\frac{4}{7}\times \frac{1}{2}=\frac{2}{7}$