Chapter 7.3, Problem 7.61E

(a)

To determine

To construct: a tree diagram to represent this chance process.

Explanation of Solution

Given:

A = first card is a heart

B = second card is a hear

With replacement condition

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Graph:

Tree diagram:-

(b)

To determine

To Calculate: the probability that both cards are hearts.

Answer to Problem 7.61E

0.1875

Explanation of Solution

Given:

Total sample space = 52 cards

Heart cards = 13 cards

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

  $\begin{array}{c}\text{P}\left(\text{A}\cap \text{B}\right)\text{=P}\left(\text{first card is a heart and second card is a heart}\right)\\ =\frac{13}{52}\times \frac{13}{52}\\ =\frac{1}{16}\\ =0.1875\end{array}$

(c)

To determine

To Explain: that the A and B events are independent.

Answer to Problem 7.61E

Yes, independent

Explanation of Solution

A and B events are independent, because drawn cards condition is with replacement means drawn cards are returned to the deck so there is no possibility that the second card is a heart is in no way affected by the first card being a heart.