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Conceptual Overview: Explore how the probability of the intersection of two events equals the probability that both events occur. The two circles shown below represent two events, A and B. The area of each circle represents the probability of each event. When the circles do not overlap, it is impossible for both events to occur at the same time. Drag one of the circles so they partially overlap. Drag on the letters 'A' and 'B' to change the size of the circles. The area of the overlap is the probability that both events occur simultaneously and its value is displayed above the rectangle as P (An B). The intersection is often described as an "AND" statement. The intersection is the probability of "A AND B" occurring simultaneously. PIAL 0.129 P(B)-0.067 PIA OBL-0

Conceptual Overview: Explore how the probability of the intersection of two events equals the probability that both events occur. The two circles shown below represent two events, A and B. The area of each circle represents the probability of each event. When the circles do not overlap, it is impossible for both events to occur at the same time. Drag one of the circles so they partially overlap. Drag on the letters 'A' and 'B' to change the size of the circles. The area of the overlap is the probability that both events occur simultaneously and its value is displayed above the rectangle as P (An B). The intersection is often described as an "AND" statement. The intersection is the probability of "A AND B" occurring simultaneously. PIAL 0.129 P(B)-0.067 PIA OBL-0

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 15PS
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Probability of the Intersection of Two Sets Conceptual Overview: Explore how the probability of the intersection of two events equals the probability that both events occur. The two circles shown below represent two events, A and B. The area of each circle represents the probability of each event. When the circles do not overlap, it is impossible for both events to occur at the same time. Drag one of the circles so they partially overlap. Drag on the letters 'A' and 'B' to change the size of the circles. The area of the overlap is the probability that both events occur simultaneously and its value is displayed above the rectangle as P (An B). The intersection is often described as an "AND" statement. The intersection is the probability of "A AND B" occurring simultaneously. P(A) = 0.129, P(B) = 0.067, P(An B) = 0 B
Transcribed Image Text:Probability of the Intersection of Two Sets Conceptual Overview: Explore how the probability of the intersection of two events equals the probability that both events occur. The two circles shown below represent two events, A and B. The area of each circle represents the probability of each event. When the circles do not overlap, it is impossible for both events to occur at the same time. Drag one of the circles so they partially overlap. Drag on the letters 'A' and 'B' to change the size of the circles. The area of the overlap is the probability that both events occur simultaneously and its value is displayed above the rectangle as P (An B). The intersection is often described as an "AND" statement. The intersection is the probability of "A AND B" occurring simultaneously. P(A) = 0.129, P(B) = 0.067, P(An B) = 0 B
NOTE: If you cannot obtain the exact values listed in the question when clicking and dragging the diagram, select the next closest value and use approximation to find the correct answer. 1. Click on the "A" in the left (orange) circle and drag until its probability is P(A)=0.061. Click on the "B" in the right (blue) circle and drag until its probability is P(B)=0.16. Place A entirely inside B. What is the value of P(An B)? a. 0.16 b. 0.22 c. 0.061 d. 0.1 -Select- 2. Leaving P(A) = 0.061 and P(B) = 0.16, move B until the value of P(A n B)=0.02. What fraction of A now intersects with B? a. 1/3 b. 1/2 c. 1 d. 3/4 -Select-
Transcribed Image Text:NOTE: If you cannot obtain the exact values listed in the question when clicking and dragging the diagram, select the next closest value and use approximation to find the correct answer. 1. Click on the "A" in the left (orange) circle and drag until its probability is P(A)=0.061. Click on the "B" in the right (blue) circle and drag until its probability is P(B)=0.16. Place A entirely inside B. What is the value of P(An B)? a. 0.16 b. 0.22 c. 0.061 d. 0.1 -Select- 2. Leaving P(A) = 0.061 and P(B) = 0.16, move B until the value of P(A n B)=0.02. What fraction of A now intersects with B? a. 1/3 b. 1/2 c. 1 d. 3/4 -Select-
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