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: Determine the sample space

When a coin is tossed twice, for each toss there are 2 possibilities (H or T).
By the multiplication principle, the total number of outcomes in the sample space \(S\) is \(2\times2 = 4\).
The sample - space \(S=\{HH, HT, TH, TT\}\).

Step2: Find the outcomes for the event that the first toss is tails

If the first toss is tails (T), then for the second toss, there are 2 possibilities (H or T).
The outcomes for the event \(E\) (first toss is tails) are \(E = \{TH, TT\}\).

Answer:

Sample space: \(HH, HT, TH, TT\)
Event that the first toss is tails: \(TH, TT\)