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: no heads on the last two tosses event c: exactly one head

Explanation:

Step1: Identify outcomes for Event A

Outcomes with two or more heads are THH, HTH, HHT, HHH.

Step2: Calculate probability for Event A

There are 4 favorable outcomes out of 8 total outcomes. Probability $P(A)=\frac{4}{8}=\frac{1}{2}$.

Step3: Identify outcomes for Event B

Outcomes with no heads on the last two tosses are TTT, HTT.

Step4: Calculate probability for Event B

There are 2 favorable outcomes out of 8 total outcomes. Probability $P(B)=\frac{2}{8}=\frac{1}{4}$.

Step5: Identify outcomes for Event C

Outcomes with exactly one head are TTH, THT, HTT.

Step6: Calculate probability for Event C

There are 3 favorable outcomes out of 8 total outcomes. Probability $P(C)=\frac{3}{8}$.

Answer:

Event	Outcomes (Checked)	Probability
Event B	TTT, HTT	$\frac{1}{4}$
Event C	TTH, THT, HTT	$\frac{3}{8}$