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: alternating tail and head (with either coming first) event b: two or more tails event c: a tail on the last toss or the second toss (or both) outcomes hhh htt thh hth tht ttt tth hht probability

Explanation:

Step1: Analyze Event A

Event A is alternating tail and head (with either coming first). For 3 - tosses, the favorable outcomes are THT and HTH.

Step2: Analyze Event B

Event B is two or more tails. The favorable outcomes are TTT, TTH, HTT, THT.

Step3: Analyze Event C

Event C is a tail on the last toss or the second toss (or both). The favorable outcomes are HTT, THT, TTT, TTH, HHT.

Step4: Calculate probabilities

The total number of possible outcomes when a coin is tossed 3 times is \(n = 2\times2\times2=8\) since each toss has 2 possibilities.
The probability of an event \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For Event A: The number of favorable outcomes \(n_A = 2\), so \(P(A)=\frac{2}{8}=\frac{1}{4}\).
For Event B: The number of favorable outcomes \(n_B = 4\), so \(P(B)=\frac{4}{8}=\frac{1}{2}\).
For Event C: The number of favorable outcomes \(n_C = 5\), so \(P(C)=\frac{5}{8}\).

Outcomes	Event A	Event B	Event C
HTT		√	√
THH
HTH	√		√
THT	√	√	√
TTT		√	√
TTH		√	√
HHT			√
Probability	\(\frac{1}{4}\)	\(\frac{1}{2}\)	\(\frac{5}{8}\)

Answer:

Outcomes	Event A	Event B	Event C
HTT		√	√
THH
HTH	√		√
THT	√	√	√
TTT		√	√
TTH		√	√
HHT			√
Probability	\(\frac{1}{4}\)	\(\frac{1}{2}\)	\(\frac{5}{8}\)