   Chapter 14.2, Problem 35E ### 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

# 3 3 - 4 0 Intersection of Events These exercises involve the probability of the intersection of events.Two cards are drawn from a deck without replacement. Find the probability of the following events.(a) The first is an ace and the second is a king.(b) Both cards are aces.

To determine

(a)

To find:

The probability that the first drawn card is an ace and the second is a king.

Explanation

Given:

Two cards are drawn from a deck without replacement.

Approach:

Probability of the intersection of events: If A and B are two mutually exclusive events in a sample space S, then the probability of A and B is,

p(AB)=p(A)p(B)(1)

Calculation:

There are 4 suits in a deck of 52 playing cards, each of the four suits, spades, diamonds, hearts, and clubs, contain 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

Jack, Queen, King are face cards, there are total 12 face cards.

Suppose E is the event that the first card is an ace and F is the event that the second card is a king.

p(E)=452

Here, p(E) is the probability of an ace in a deck of 52 playing cards.

p(F)=451

Here, p(F) is the probability of a king after drawing an ace from the deck

To determine

(b)

To find:

The probability that both cards are aces.

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