A fair coin is tossed 4 times 7 How many outcomes are there

A fair coin is tossed 4 times.
7. How many outcomes are there in the sample space? (5 pts)
8. What is the probability that the third toss is heads, given that the first toss is heads? (10 pts)
9. 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? (5 pts)

Solution

similar problem A coin is tossed 7 times. Let A be the event that the first toss is heads. Let B be the event that the fifth toss is heads. Are A and B mutually exclusive? Why or why not? Are A and B independent? Why or why not? Are A and B mutually exclusive? Why or why not? No because there are a slew of sequences of 7 tosses that have heads on the 1st and heads on the 5th toss. Are A and B independent? Why or why not? Yes because the P(head) on 1st = 1/2 and P(head on 5th) = 1/2 and P(A nd B) = P(A)*P(B) = 1/4