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 third toss is heads. 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 third toss is heads:

Explanation:

Step1: List all possible outcomes for three - coin tosses

For each toss, there are 2 possibilities (H or T). Using the multiplication principle, the total number of outcomes for three tosses is \(2\times2\times2 = 8\).
The sample space \(S=\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}\)

Step2: Select outcomes where the third toss is heads

We look at each element of the sample space. If the third character is 'H', we include it.
The event \(E=\{HHH, HTH, THH, TTH\}\)

Answer:

Sample space: \(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\)
Event that the third toss is heads: \(HHH, HTH, THH, TTH\)