When a balanced dime is tossed three times, eight equally likely outcomes are possible:
HHH ...... HTH ......THH ......TTH
HHT ....... HTT ......THT .......TTT
Let
A = event the first toss is heads,
B = event the third toss is tails, and
C = event the total number of heads is 1.
a. Compute P(A), P(B), and P(C).
b. Compute P(B | A).
c. Are A and B independent events? Explain your answer.
d. Compute P(C | A).
e. Are A and C independent events? Explain your answer.