   Chapter 14.CR, Problem 7CC ### 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) What is meant by the conditional probability of E given F? How is this probability calculated?(b) What are independent events?(c) If E and F are independent events, what is the probability of E and F occurring? What if E and F are not independent?(d) A jar contains 3 white and 7 black balls. Let E be the event “the first ball drawn is black” and let F be the event “the second ball drawn is black.”(i) Find P ( E ∩ F ) if the balls are drawn with replacement.(ii) Find P ( E ∩ F ) if the balls are drawn without replacement.

To determine

(a)

To explain:

The meaning of the conditional probability of E given F, and give formula.

Explanation

Approach:

The conditional probability is the probability that E occurs if we know that F has occurred and given by,

P(E|F)=p(EF)P(F)

To determine

(b)

To explain:

The independent events.

To determine

(c)

To find:

The probability of two independent and no independent events E and F.

To determine

(d)

To find:

The value of P(EF), and the value of P(EF) for the given condition.

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