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 heads
event b: a tail on the second toss or the third toss (or both)
event c: a head on each of the last two tosses

Explanation:

Step1: Calculate probability for Event A

Count outcomes with two or more heads. Outcomes are \(HHH\), \(HHT\), \(THH\), \(HTH\). Number of favorable outcomes \(n = 4\). Total outcomes \(N=8\). Probability \(P(A)=\frac{n}{N}\).
$$P(A)=\frac{4}{8}=\frac{1}{2}$$

Step2: Calculate probability for Event B

Count outcomes with a tail on second or third toss. Outcomes are \(HHT\), \(TTT\), \(HTT\), \(TTH\), \(THH\), \(HTH\), \(THT\). Number of favorable outcomes \(n = 7\). Total outcomes \(N = 8\). Probability \(P(B)=\frac{n}{N}\).
$$P(B)=\frac{7}{8}$$

Step3: Calculate probability for Event C

Count outcomes with head on last two tosses. Outcomes are \(HHH\), \(THH\). Number of favorable outcomes \(n = 2\). Total outcomes \(N=8\). Probability \(P(C)=\frac{n}{N}\).
$$P(C)=\frac{2}{8}=\frac{1}{4}$$

Answer:

Event A: \(\frac{1}{2}\)
Event B: \(\frac{7}{8}\)
Event C: \(\frac{1}{4}\)