Question

a coin will be tossed twice, 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 first toss is tails. use the format ht to mean that the first toss is heads and the second is tails. if there is more than one element in the set, separate them with commas. sample space: event that the first toss is tails:

Explanation:

Step1: List all possible outcomes for two - coin tosses

For the first toss, there are 2 possibilities (heads or tails), and for each of these, the second toss also has 2 possibilities. So the sample space is all combinations: $HH, HT, TH, TT$.

Step2: Identify outcomes with first - toss as tails

We look for combinations where the first letter is $T$. The outcomes are $TH, TT$.

Answer:

Sample space: $HH, HT, TH, TT$
Event that the first toss is tails: $TH, TT$