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 a 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. outcomes probability hhh thh htt tht tth hht ttt hth event a: no tails on the first two tosses event b: a tail on the first toss or the second toss (or both) event c: a tail on the first toss

Explanation:

Step1: Identify Event A outcomes

Event A: No tails on first two tosses → first two are H. Valid outcomes: HHH, HHT. Count = 2. Probability = $\frac{2}{8} = \frac{1}{4}$.

Step2: Identify Event B outcomes

Event B: Tail on first or second toss. Invalid outcomes (no tail on first/second): HHH, HHT. Valid count = 8 - 2 = 6. Probability = $\frac{6}{8} = \frac{3}{4}$.

Step3: Identify Event C outcomes

Event C: Tail on first toss → first character T. Valid outcomes: THH, THT, TTH, TTT. Count = 4. Probability = $\frac{4}{8} = \frac{1}{2}$.

Answer:

Event	Checked Outcomes	Probability
B	THH, HTT, THT, TTH, TTT, HTH	$\frac{3}{4}$
C	THH, THT, TTH, TTT	$\frac{1}{2}$