Question

a coin is tossed three times. an outcome is represented by a string of the sort htt (meaning a head on the first toss, followed by two tails). the 8 outcomes are listed in the table below. note that each outcome has the same probability. for each of the three events in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event. event a: two or more tails event b: a head on each of the last two tosses event c: a tail on the second toss

Explanation:

Step1: Determine outcomes for Event A

Count outcomes with 2 or 3 tails. Outcomes are TTT, TTH, THT, HTT.

Step2: Calculate probability of Event A

Since there are 4 favorable outcomes out of 8 total outcomes, probability is $\frac{4}{8}=\frac{1}{2}$.

Step3: Determine outcomes for Event B

Find outcomes with head on last two tosses. Outcomes are HHH, THH.

Step4: Calculate probability of Event B

There are 2 favorable outcomes out of 8, so probability is $\frac{2}{8}=\frac{1}{4}$.

Step5: Determine outcomes for Event C

Find outcomes with tail on second - toss. Outcomes are HTT, TTT, HTH, TTH.

Step6: Calculate probability of Event C

There are 4 favorable outcomes out of 8, so probability is $\frac{4}{8}=\frac{1}{2}$.

Answer:

Event A: TTT, TTH, THT, HTT; $\frac{1}{2}$
Event B: HHH, THH; $\frac{1}{4}$
Event C: HTT, TTT, HTH, TTH; $\frac{1}{2}$