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A special deck of cards has ten cards. Four are green (G), two are blue (B), and four 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).
Part (a)
List the sample space. (Enter your answer using letter combinations separated by commas. Example: GH, GT, ...)
Part (b)
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) =
Part (c)
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 mutually exclusive because they happen at the same time. Thus, P(A and B) = .
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 mutually exclusive because they happen at the same time. Thus, P(A and C) = .
