a coin is tossed three times. an outcome is represented by a string of the sort htt (meaning a head on the…

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: a head on each of the last two tosses event b: alternating head and tail (with either coming first) event c: a tail on the last toss

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: a head on each of the last two tosses event b: alternating head and tail (with either coming first) event c: a tail on the last toss

Answer

Explanation:

Step1: Identify total number of outcomes

There are 8 total outcomes when a coin is tossed 3 - times.

Step2: Determine outcomes for Event A

Event A: A head on each of the last two tosses. The outcomes are HHH, THH. So there are 2 favorable outcomes. Probability of Event A = $\frac{2}{8}=\frac{1}{4}$.

Step3: Determine outcomes for Event B

Event B: Alternating head and tail (with either coming first). The outcomes are THT, HTH. So there are 2 favorable outcomes. Probability of Event B = $\frac{2}{8}=\frac{1}{4}$.

Step4: Determine outcomes for Event C

Event C: A tail on the last toss. The outcomes are THT, TTH, HTT, TTT. So there are 4 favorable outcomes. Probability of Event C = $\frac{4}{8}=\frac{1}{2}$.

Event THT TTH HTH HHT HTT HHH THH TTT Probability
A √ √ $\frac{1}{4}$
B √ √ $\frac{1}{4}$
C √ √ √ √ $\frac{1}{2}$

Answer:

Event THT TTH HTH HHT HTT HHH THH TTT Probability
A √ √ $\frac{1}{4}$
B √ √ $\frac{1}{4}$
C √ √ √ √ $\frac{1}{2}$