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	\
	htt	hth	thh	hht	tth	tht	ttt	hhh		\
event a: a tail on the first toss or the second toss (or both)	□	□	□	□	□	□	□	□	□	\
event b: no tails on the last two tosses	□	□	□	□	□	□	□	□	□	\
event c: a head on each of the last two tosses	□	□	□	□	□	□	□	□	□

Explanation:

Step1: Identify Event A outcomes

First toss T or second toss T: TTH, THT, TTT, HTT, HTH, THH, TTH (corrected: all except HHT, HHH? Wait no: first toss T: TTH, THT, TTT, THH; second toss T: HTT, HTH, TTH, THT. Combine: TTH, THT, TTT, THH, HTT, HTH → 6 outcomes.

Step2: Calculate Event A probability

$\frac{6}{8} = \frac{3}{4}$

Step3: Identify Event B outcomes

Last two tosses no tails (both H): THH, HHH → 2 outcomes.

Step4: Calculate Event B probability

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

Step5: Identify Event C outcomes

Last two tosses both H: THH, HHH → 2 outcomes.

Step6: Calculate Event C probability

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

Answer:

Event A probability: $\frac{3}{4}$
Event B probability: $\frac{1}{4}$
Event C probability: $\frac{1}{4}$

(Note: For checkboxes:
Event A: Check TTH, THT, TTT, THH, HTT, HTH
Event B: Check THH, HHH
Event C: Check THH, HHH)