A special deck of cards has ten cards. Three are green (G), four are blue (B), and three are red (R). When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin, which lands on heads (H) or tails (T). 1. List the sample space. (Enter your answer using letter combinations separated by commas. Example: GH, GT, ...) 2. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A). (Enter your probability as a fraction.) P(A) = 3. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. (Enter your probability as a fraction.) 4. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. (Enter your probability as a fraction.) A and B  are are not mutually exclusive because they can cannot happen at the same time. Thus, P(A and B) =   5. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. (Enter your probability as a fraction.) A and C  are are not mutually exclusive because they can cannot happen at the same time. Thus, P(A and C) =

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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A special deck of cards has ten cards. Three are green (G), four are blue (B), and three are red (R). When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin, which lands on heads (H) or tails (T).

1. List the sample space. (Enter your answer using letter combinations separated by commas. Example: GH, GT, ...)

2. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A). (Enter your probability as a fraction.)
P(A) =

3. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. (Enter your probability as a fraction.)

4. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. (Enter your probability as a fraction.)
A and B  are are not mutually exclusive because they can cannot happen at the same time. Thus,
P(A and B) =
 
5. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. (Enter your probability as a fraction.)
A and C  are are not mutually exclusive because they can cannot happen at the same time. Thus,
P(A and C) =
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