Question

a coin will be tossed three times, and each toss will be recorded as heads (h) or tails (t). give the sample space describing all possible outcomes. then give all of the outcomes for the event that the second toss is tails. use the format hth to mean that the first toss is heads, the second is tails, and the third is heads. if there is more than one element in the set, separate them with commas. sample space: {} event that the second toss is tails: {}

Explanation:

Step1: List all 3-toss outcomes

Each toss has 2 results, so total outcomes: $2^3=8$. The full set is: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Step2: Filter outcomes with second T

Select outcomes where the second character is T: HTH, HTT, TTH, TTT

Answer:

Sample space: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Event that the second toss is tails: {HTH, HTT, TTH, TTT}