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: exactly one head event b: two or more heads event c: a tail on the first toss

Explanation:

Step1: Identify outcomes for Event A

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

Step2: Calculate probability of Event A

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

Step3: Identify outcomes for Event B

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

Step4: Calculate probability of Event B

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

Step5: Identify outcomes for Event C

Outcomes with a tail on the first - toss are THT, TTT, TTH.

Step6: Calculate probability of Event C

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

Answer:

Event	THT	THH	HTT	TTT	HHH	HTH	TTH	HHT	Probability
Event B: Two or more heads		$\boxed{\checkmark}$			$\boxed{\checkmark}$	$\boxed{\checkmark}$		$\boxed{\checkmark}$	$\frac{1}{2}$
Event C: A tail on the first toss	$\boxed{\checkmark}$			$\boxed{\checkmark}$			$\boxed{\checkmark}$		$\frac{1}{2}$