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 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 third toss is tails: {}

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 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 third toss is tails: {}

Answer

Answer:

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

Explanation:

Step1: List all possibilities for 1 - st toss

For the first coin - toss, there are 2 possibilities (H or T).

Step2: Combine with 2 - nd toss

For each outcome of the first toss, the second toss also has 2 possibilities. So there are (2\times2 = 4) combinations for the first two tosses: HH, HT, TH, TT.

Step3: Combine with 3 - rd toss

For each of the 4 combinations of the first two tosses, the third toss has 2 possibilities. So the sample - space has (2\times2\times2=8) elements: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Step4: Select outcomes with third - toss as tails

We go through the sample - space and pick out the outcomes where the third element is T. These are HHT, HTT, THT, TTT.