Chapter 13, Problem 13PT

To determine

Find the probability that the first marble is brown and second is not purple.Whether the eventis an dependent or independent.

Answer to Problem 13PT

The events are dependent because the happening of one depends on the other, and the probability that the first is brown and second is notpurple is $\frac{1}{60}$ .

Explanation of Solution

Given information: A hat has 6 green, 2 red, 2 brown, 4 navy and 2 purple marbles from which 2 marbles without replacement are picked.

Calculation: Since the two marbles are picked without replacementin which the brown marble is not replaced before the second one, therefore these two events are dependent. Therefore the probability that the first marble is brown and second is notpurple is evaluated as,

  $\begin{array}{c}P\left(\text{brown and not purple}\right)=P\left(\text{brown}\right)\times P\left(\text{not purple}\right)\\ =\frac{2}{16}\times \frac{2}{15}\\ =\frac{1}{60}\end{array}$