a coin will be tossed three times, and each toss will be recorded as heads (h) or tails (t). give the sample…

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:

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:

Answer

Explanation:

Step1: List all possible combinations for 3 - coin tosses

Each coin - toss has 2 possibilities (heads or tails). For 3 coin - tosses, we use the multiplication principle. The sample space is found by considering all possible sequences of heads and tails. The sample space $S={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}$.

Step2: Select outcomes where the third toss is heads

We go through the sample - space and pick out the outcomes where the third element of the sequence is 'H'. The event $E$ (third toss is heads) $={HHH, HTH, THH, TTH}$.

Answer:

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