## An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the

Question

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.​

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4 weeks 2021-08-16T15:45:56+00:00 2 Answers 0 views 0

1. ➡️Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.

➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

➡️The following problem can be divided in two cases

➡️(i) The number on the die is even.

➡️The sample space SE={(2,H),(4,H),(6,H),(2,T),(4,T),(6,T)}

➡️(ii) The number on the die is odd and the coin is tossed twice

➡️The sample space

➡️So = {(1,H,H), (3,H,H), (5,H,H), (1,H,T), (3,H,T), (5,H,T), (1,T,H), (3,T,H), (5,T,H), (1,T,T), (3,T,T), (5,T,T)}

➡️Hence, the overall sample space for the problem= SE + So

➡️S = {(2,H), (4,H), (6,H), (2,T), (4,T), (6,T), (1,H,H), (3,H,H), (5,H,H), (1,H,T), (3,H,T), (5,H,T), (1,T,H), (3,T,H), (5,T,H), (1,T,T), (3,T,T), (5,T,T)}

Step-by-step explanation:

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An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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➡️Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.

➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

➡️The following problem can be divided in two cases

➡️(i) The number on the die is even.

➡️The sample space SE={(2,H),(4,H),(6,H),(2,T),(4,T),(6,T)}

➡️(ii) The number on the die is odd and the coin is tossed twice

➡️The sample space

➡️So = {(1,H,H), (3,H,H), (5,H,H), (1,H,T), (3,H,T), (5,H,T), (1,T,H), (3,T,H), (5,T,H), (1,T,T), (3,T,T), (5,T,T)}

➡️Hence, the overall sample space for the problem= SE + So

➡️S = {(2,H), (4,H), (6,H), (2,T), (4,T), (6,T), (1,H,H), (3,H,H), (5,H,H), (1,H,T), (3,H,T), (5,H,T), (1,T,H), (3,T,H), (5,T,H), (1,T,T), (3,T,T), (5,T,T)}

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