A special deck of cards has ten cards. One is green (G), three are blue (B), and

Question

A special deck of cards has ten cards. One is green (G), three are blue (B), and six 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). O Part (a) List the sample space. (Enter your answer using letter combinations separated by commas. Example: GH, GT,. GH, GT, BH, BT, BH, BT, BH, BT, RH, RT, RH, O 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.) PIA)3/20 E 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 cannot . happen at the same time. Thus, PA and B- 0 are O Part (d) 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 not mutually exclusive because they canh happen at the same time. Thus, PIA and C)1

Explanation / Answer

Sol:

Here picking red or blue is independent not mutually exclusive

P(A and C)=P(A).P(C)

put this option

Thus P(A and C) is not 1

Mark

P(A and C)=P(A).P(C)

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