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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

2 7 - 3 2 Conditional Probability These exercises involve conditional probability.

A die is rolled. Find the given conditional probability.

(a) A “five” shows, given that the number showing is greater than 3 .

(b) A “three’ shows given that the number showing is odd.

To determine

(a)

To find:

The conditional probability that the die shows “five” given that the number showing is greater than 3.

Explanation

Given:

A die is rolled and the number showing is greater than 3.

Approach:

The probability of an event A is given as,

p(A)=n(A)n(S)(1)

Here, n(E) is the number of favorable outcomes in event E and n(S) is the total number of outcomes.

The conditional probability is given as,

p(A|B)=p(AB)p(B)(2)

Here, p(A|B) is the conditional probability of an event A given that B has already occurred, p(AB) is the joint probability of events A and B, p(B) is the probability of event B.

Calculation:

There are total six numbers in a die as 1, 2, 3, 4, 5, and 6. Then,

n(S)=6

The numbers which are greater than 3 on a die are 4, 5, and 6. Then,

n(numbers >3)=3

Here, n(numbers >3) is the total number of the numbers greater than three on a die.

Substitute 3 for n(numbers >3) and 6 for n(S) in equation (1). Then,

p(numbers>3)=36

Here, p(numbers>3) is the probability of numbers greater than 3 on a die.

p(5)=16

Here, p(5) is the probability of 5 on rolling a die

To determine

(b)

To find:

The conditional probability that the die shows “three” given that the number showing is odd.

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