Chapter 13, Problem 12PT

To determine

Find the probability that the first card is pink and the second card is pink.

Answer to Problem 12PT

The events are independent because the happening of one does not affect the other, and the probability that the first is pink and second is also pink is $\frac{1}{9}$ .

Explanation of Solution

Given information: The deck of cards has 5 yellow, 5 pink and 5 orange cards from which 2 cards are chosen with the replacement.

Calculation: Since the cards are chosen with replacement and the happening of first does not affect the other event, therefore these two events are independent. Therefore the probability that the first card is pink and second is also pink is evaluated as,

  $\begin{array}{c}P\left(\text{pink and then pink}\right)=P\left(\text{pink}\right)\times P\left(\text{pink}\right)\\ =\frac{5}{15}\times \frac{5}{15}\\ =\frac{1}{9}\end{array}$