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Chapter 5: Q. 102. (page 337)

Matching suits A standard deck of playing cards consists of 52 cards with 13 cards in each of four suits: spades, diamonds, clubs, and hearts. Suppose you shuffle the deck thoroughly and deal 5 cards face-up onto a table.

a. What is the probability of dealing five spades in a row?

b. Find the probability that all 5 cards on the table have the same suit.

Short Answer

Expert verified

The required answers are:

Part a) The probability is 0.0004952.

Part b) The probability is0.001981.

Step by step solution

01

Part a) Step 1: Given information

Given that,

Number of cards in a deck =52

Number of cards in each suit=13

02

Part a) Step 2: Calculation

The probability of taking five spades can be calculated using the following formula:

P(fivespades)=1352×1251×1150×1049×948=154440311875200=0.0004952

Therefore, the required probability is0.0004952

03

Part b) Step 1: Explanation

The likelihood of all five cards being of the same suit can be calculated as follows:

P(sameunits)=p(5spades)+P(5hearts)+P(5diamonds)+P(5clubs)=3366640+3366640+3366640+3366640=0.001981

Therefore, the required probability is0.001981.

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