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. \

	outcomes	probability	\
	hht	hth	tht	tth	thh	htt	ttt	hhh		\
event a: a tail on the first toss or the third toss (or both)	☐	☐	☐	☐	☐	☐	☐	☐	☐	\
event b: two or more tails	☐	☐	☐	☐	☐	☐	☐	☐	☐	\
event c: a head on each of the first two tosses	☐	☐	☐	☐	☐	☐	☐	☐	☐

Explanation:

Step1: List all 8 outcomes

Total outcomes: HHT, HTH, THT, TTH, THH, HTT, TTT, HHH (each probability $\frac{1}{8}$)

Step2: Find Event A outcomes

Event A: First or third toss tail. Outcomes: THT, TTH, THH, HTT, TTT, HTH, TTH? Correction: Correct outcomes with first toss T (THT, TTH, THH, TTT) or third toss T (HTT, THT, TTH, HHT) → Unique: THT, TTH, THH, HTT, TTT, HTH, HHT (7 outcomes)

Step3: Calculate Event A probability

$7 \times \frac{1}{8} = \frac{7}{8}$

Step4: Find Event B outcomes

Event B: ≥2 tails. Outcomes: THT, TTH, HTT, TTT (4 outcomes)

Step5: Calculate Event B probability

$4 \times \frac{1}{8} = \frac{1}{2}$

Step6: Find Event C outcomes

Event C: First two tosses head. Outcomes: HHT, HHH (2 outcomes)

Step7: Calculate Event C probability

$2 \times \frac{1}{8} = \frac{1}{4}$

Answer:

Event A probability: $\frac{7}{8}$
Event B probability: $\frac{1}{2}$
Event C probability: $\frac{1}{4}$