   Chapter 14.2, Problem 19E ### 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 five-card poker hand is drawn from a standard 52-card deck. Find the probability of the following events.a) At least one card is a spade.b) At least one card is a face card.

To determine

(a)

To find:

The probability that at least one card is a spade.

Explanation

Given:

5-card poker hand is drawn at from a standard 52-card deck.

Approach:

Formula for finding the probability is P(A)=n(A)n(S) ...(1).

Here P(A) denotes the probability of the event A, n(A) is the favourable outcome of A, n(S) is the total outcome.

The combination formula is Cnr=n!(nr)!r! where 0rn.

Calculation:

Let A be the event that at least one card is a spade.

n(A)=C131×C394+C132×C393+C133×C392+C134×C391+C135×C390, n(S)=C525

Substituting n(A)=C131×C394+C

To determine

(b)

To find:

The probability that at least one card is a face card

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