Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.

What is P(A), the probabillity that the six-sided die is an even number?

What is P(B), the probability of the four-sided die is an odd number?

What is P(A and B), the probability that the six-sided die is an even number and the four-sided die is an odd number?

Are events A and B independent?

a) Yes, events A and B are independent events.

b) No, events A and B are not independent events.

Answer: P(A) = 1/2

P(B) = 1/2

P(A and B) = 1/4

a) Yes, events A and B are independent events.

Step-by-step explanation: The event A is related to a six-sided die, so total possibilities is 6.

For a six-sided die to show a even number, there are 3 possibilities: (2,4,6)

so, P(A) = 3/6 = 1/2

The event B is for a 4-sided die, i.e. total possibilities is 4.

To show an odd number, there are 2 possibilities: (1,3).

Then, P(B) = 2/4 = 1/2

Now, the probability of occuring A and B is:

P(A and B) = P(A).P(B)

P(A and B) = 1/2*1/2

P(A and B) = 1/4

The events are independent events because the probability of A happening does not influence the occuring of event B.

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