an experiment consist of first rolling die and them tossing a coin | Wyzant Ask An Expert

An experiment consists of first rolling a die and then tossing a coin.

(a) List the sample space.

  1. {(3, H), (4, H)}
  2. {(3, H), (3, T), (4, H), (4, T)}
  3. {(1, T), (2, T), (3, T), (4, T), (5, T), (6, T)}
  4. {(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}
  5. {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H)}

(b) Let A be the event that either a three or a four is rolled first, followed by landing a head on the coin toss. Find P(A). (Enter your probability as a fraction.)

P(A) = ______

(c) Suppose that a new experiment consists of first rolling a die and then tossing a coin twice. Let B be the event that the first and second coin tosses land on heads. Let C be the event that either a three or a four is rolled first, followed by landing a head on the first coin toss. Are the events B and C mutually exclusive? Explain your answer.

  1. Events B and C are mutually exclusive because they have different probabilities.
  2. Events B and C are mutually exclusive because the first and second coin tosses cannot land on heads when a three or four is rolled first.
  3. Events B and C are not mutually exclusive because the first and second coin tosses can land on heads when a three or four is rolled first.
  4. Events B and C are mutually exclusive because they are dependent events.

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