**Question 2** (1 point)Let \( A \) and \( B \) be events in a sample space \( S \) such that \( P(A) = 0.4 \) and \( P(B \mid A) = 0.2 \). Find \( P(A \cap B) \).Choices:- \( P(A \cap B) = 0.99 \)- \( P(A \cap B) = 0.97 \)- \( P(A \cap B) = 0.08 \)- \( P(A \cap B) = 0.25 \)**Explanation:**To solve for \( P(A \cap B) \), you can use the formula for conditional probability:\[ P(B \mid A) = \frac{P(A \cap B)}{P(A)} \]Given:\( P(A) = 0.4 \)\( P(B \mid A) = 0.2 \)Substitute the values into the formula:\[ 0.2 = \frac{P(A \cap B)}{0.4} \]Solving for \( P(A \cap B) \):\[ P(A \cap B) = 0.2 \times 0.4 = 0.08 \]Correct choice: \( P(A \cap B) = 0.08 \)

Answered: Let A and B be events in a sample space…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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K rch Write out the sample space and assume each outcome is equally likely. Then give the probability of the requested outcomes. A man is shopping for a new patio umbrella. There is a 9-foot and a 12-foot model, and each is available in gray, forest green, and white. (a) He buys a 12-foot forest green umbrella. (b) He buys a 9-foot umbrella. (c) He buys a gray-colored umbrella. Write out the sample space. Choose the correct answer below. OA. {(9-foot, gray), (9-foot, forest green), (9-foot, white), (12-foot, gray), (12-foot, forest green), (12-foot, white)} OB. {(9-foot, 12-foot), (gray, forest green), (forest green, white), (gray, white)} OC. {(9-foot, gray), (9-foot, forest green), (9-foot, white), (12-foot, gray), (12-foot, forest green)} OD. Ø (a) He buys a 12-foot forest green umbrella. The probability is (Type an integer or a simplified fraction.) O t ... er (DELL) Time Remaining: 01:36:59 66°F @ 3 Next 2:27 PM 12/3/2022
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Let A and B be events in a sample space S such that P(A) = 21/100, P(B) = 2/5, and P(AB) = 13/100. Find P( B | Ac ). A) 0.3148 B) 0.5250 C) 0.5063 D) 0.1646 E) 0.6750

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Let A and B be events in a sample space S such that P(A) = .4 and P(BA) = 2. Find: P(ANB). OP(AB)-0.99 O PAB)-0.97 O PAB)-0.08 OPAB)-0.25 Finder 2 NOV 11