   Chapter 14.2, Problem 15E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# A poker hand, consisting of five cards, is dealt from a standard deck of 52 cards. Find the probability that the hand contains the cards described.(a) Five hearts(b) Five cards of the same suit(c) Five face cards(d) An ace, king, queen, jack, and a ten, all of the same suit (royal flush)

To determine

(a)

To find:

The probability that the hand contains five hearts.

Explanation

Given:

A poker hand contains five cards selected from the standard deck of 52 cards and the event is of selecting five heart cards.

Approach:

The number of combinations of n distinct objects taken r at a time is,

C(n,r)=n!r!(nr)!;(rn).

Let S be the sample space of an experiment and let E be an event. Then the probability of E, denoted as, P(E) and given by,

P(E)=n(E)n(S)(1)

Here,

n(E)n(S)=numberofelementsinEnumberofelementsinS

Calculation:

The experiment is that a poker hand consisting of five cards from a standard deck of 52 cards,

Thus, the number of elements in the sample space S is C(52,1)

To determine

(b)

To find:

The probability that a poker hand contains five cards of the same suit.

To determine

(c)

To find:

The probability that a poker hand contains five face cards.

To determine

(d)

To find:

The probability that a poker hand contains an ace, king, queen, jack, and a ten, all of the same suit.

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