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: exactly one head event b: alternating head and tail (with either coming first) event c: two or more heads

Explanation:

Step1: Calculate probability for Event A

Total outcomes \( n = 8 \).
For Event A (exactly one head), outcomes are \( TTH, THT, HTT \). So \( m_A=3 \).
Probability \( P(A)=\frac{m_A}{n}=\frac{3}{8} \).

Step2: Calculate probability for Event B

For Event B (alternating head and tail), outcomes are \( THT, HTH \). So \( m_B = 2 \).
Probability \( P(B)=\frac{m_B}{n}=\frac{2}{8}=\frac{1}{4} \).

Step3: Calculate probability for Event C

For Event C (two or more heads), outcomes are \( THH, HTH, HHT, HHH \). So \( m_C=4 \).
Probability \( P(C)=\frac{m_C}{n}=\frac{4}{8}=\frac{1}{2} \).

Answer:

Event A: Probability is \(\frac{3}{8}\)
Event B: Probability is \(\frac{1}{4}\)
Event C: Probability is \(\frac{1}{2}\)