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Marcus has a bag that contains 5 identically shaped boxes. 3 of the boxes are blue, and 2 are green. 2 of the blue boxes have a prize , and 1 of the green boxes has a prize. Marcus randomly selects a box from the bag. Let A be the event that he selects a blue box and B be the event that the box contains a prize. Which of the following statements are true?

Marcus has a bag that contains 5 identically shaped boxes. 3 of the boxes are blue, and 2 are green. 2 of the blue boxes have a prize , and 1 of the green boxes has a prize. Marcus randomly selects a box from the bag. Let A be the event that he selects a blue box and B be the event that the box contains a prize. Which of the following statements are true?

A First Course in Probability (10th Edition)
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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Marcus has a bag that contains 5 identically shaped boxes. 3 of the boxes are blue, and 2 are green. 2 of the blue boxes have a prize , and 1 of the green boxes has a prize. Marcus randomly selects a box from the bag. Let A be the event that he selects a blue box and B be the event that the box contains a prize. Which of the following statements are true? Choose all answers that apply: P(A| B) = P(A), the conditional probability that Marcus selects a blue box given that he has chosen a box with a prize is equal to the probability that Marcus selects a blue box. P(B| A) = P(B), the conditional probability that Marcus selects a box with a prize given that he has chosen a blue box is equal to the probability that Marcus selects a box with a prize. Events A and B are independent events. The outcomes of events A and B are dependent on each other. P(A and B) = P(A) · P(B), the probability that Marcus selects a box that is blue and %3D E contains a prize is equal to the probability that Marcus selects a blue box multiplied by the probability that he selects a box with a prize.
Transcribed Image Text:Marcus has a bag that contains 5 identically shaped boxes. 3 of the boxes are blue, and 2 are green. 2 of the blue boxes have a prize , and 1 of the green boxes has a prize. Marcus randomly selects a box from the bag. Let A be the event that he selects a blue box and B be the event that the box contains a prize. Which of the following statements are true? Choose all answers that apply: P(A| B) = P(A), the conditional probability that Marcus selects a blue box given that he has chosen a box with a prize is equal to the probability that Marcus selects a blue box. P(B| A) = P(B), the conditional probability that Marcus selects a box with a prize given that he has chosen a blue box is equal to the probability that Marcus selects a box with a prize. Events A and B are independent events. The outcomes of events A and B are dependent on each other. P(A and B) = P(A) · P(B), the probability that Marcus selects a box that is blue and %3D E contains a prize is equal to the probability that Marcus selects a blue box multiplied by the probability that he selects a box with a prize.
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