Refer to the following information for Questions A B and C P

Refer to the following information for Questions A, B, and C. PLEASE SHOW ALL WORK. Just the answer, without supporting work, will receive no credit.

A fair coin is tossed 4 times.

A. How many outcomes are there in the sample space?

B. What is the probability that the third toss is heads, given that the first toss is heads?

C. Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A and B independent? Why or why not?

PLEASE SHOW ALL WORK!!!! :)

Solution

a)

There are 2^4 = 16 outcomes. [ANSWER]

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b)

Coin tosses are independent of each other. Thus, it doesn\'t matter what the first toss is, so

P(3rd is heads) = 1/2 or 0.5 [ANSWER]

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c)

Yes, THEY ARE INDEPENDENT, because they don\'t influence the probability of each other happening. [ANSWER]