# The solution discusses the sample space and probabilities of die

Question 3

An experiment consists of rolling one die. Let A be event that the die shows more than one, B be event that the die shows more than 4, and C be event that die shows an even number.

a) List the sample space of this experiment.

b) Find P(A), P(B), P(C)

c) Find P(A or C), P(A or B), P(A and C), P(B and C)

d) Are A and C independent? Defend your answer.

e) Are B and C independent? Defend your answer.

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#### Solution Preview

An experiment consists of rolling one die. Let A be event that the die shows more than one, B be event that the die shows more than 4, and C be event that die shows an even number.

a) List the sample space of this experiment.

Since there are 6 probabilities while rolling a die, we can show the sample space as below:

S = {1, 2, 3, 4, 5, 6}

b) Find P (A), P (B), P(C)

Since A is the event that the die shows more than 1, the die may show 2, 3, 4, 5 or 6. Since each number has a probability of 1/6, P (A) will be the sum of their probabilities:

P (A) = P (2) + P (3) + P (4) + P (5) ...

#### Solution Summary

The solution solves for the sample spaces and the probabilities.