Chapter 5.3, Problem 102E

a)

To determine

To find: The probability of taking five spades.

Answer to Problem 102E

The probability is 0.0004952.

Explanation of Solution

Given:

Number of cards in a deck = 52

Number of cards in each suit = 13

Calculation:

The probability of taking five spades can be calculated as:

  $\begin{array}{c}P\left(\text{Five spades}\right)=\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}\times \frac{10}{49}\times \frac{9}{48}\\ =\frac{154440}{311875200}\\ =0.0004952\end{array}$

Thus, the required probability is 0.0004952.

b)

To determine

To find: The probability that all 5 cards are of same suit.

Answer to Problem 102E

The probability is 0.001981.

Explanation of Solution

The probability that all 5 cards are of same suit can be calculated as:

  $\begin{array}{c}P\left(\text{Same suit}\right)=P\left(5\text{ spades}\right)+P\left(5\text{ Hearts}\right)+P\left(5\text{ Diamonds}\right)+P\left(5\text{ clubs}\right)\\ =\frac{33}{66640}+\frac{33}{66640}+\frac{33}{66640}+\frac{33}{66640}\\ =\frac{132}{66640}\\ =0.001981\end{array}$

Thus, the required probability is 0.001981.