Solution Found!
A deck of six cards consists of three black cards numbered
Chapter , Problem 1(choose chapter or problem)
A deck of six cards consists of three black cards numbered 1, 2, 3, and three red cards numbered 1, 2, 3. First, Vann draws a card at random and without replacement. Then Paul draws a card at random and without replacement from the remaining cards. Let A be the event that Paul's card has a larger number than Vann's card. Let B be the event that Vann's card has a larger number than Paul's card.
(a) Are A and B mutually exclusive?
(b) Are A and B complements of one another?
Questions & Answers
QUESTION:
A deck of six cards consists of three black cards numbered 1, 2, 3, and three red cards numbered 1, 2, 3. First, Vann draws a card at random and without replacement. Then Paul draws a card at random and without replacement from the remaining cards. Let A be the event that Paul's card has a larger number than Vann's card. Let B be the event that Vann's card has a larger number than Paul's card.
(a) Are A and B mutually exclusive?
(b) Are A and B complements of one another?
ANSWER:Step 1 of 3
(a) If the joint occurrence of two events E and F is impossible, we say that E and F are mutually exclusive. Thus E and F are mutually exclusive if the occurrence of E precludes the occurrence of F, and vice versa.
The events are actually disjointed because any outcome in which Paul’s card has a larger number than Vann’s card couldn’t possibly also be an outcome in which Vann’s card has a larger number than Paul’s card.
Consider,
V = Van
P = Paul
r = red card
b = black card
1,2,3 = cards numbers
Event A = Paul’s card has larger number
Event B = Vann’s card has larger number