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 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.

Answer 1

Answer:

Sample space:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Third toss is heads:

{HHT, HTT, THT, TTT}

First toss is heads, second tails and third heads:

{HTH}

Explanation:

In order to find the sample space we need to write all the possible outcomes from tossing the coin three times.You can start by writting all the possible outcomes for the first toss being a head and finish with all the possible outcomes for the first toss being Tails. The number of elements in the sample space can be found by multiplying the possible outcomes of each toss together, so 2*2*2=8

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For the third toss being heads we will have one restriction this time. Which is that the third toss is Tails. You can take the elements from the sample space where the third element is a tails. In this case, the number of elements can be calculated by multiplying the possible outcomes for only the first two tosses 2*2=4

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For first toss is heads, second tails and third heads there is only one possible way for you to get this outcome so there is only one element to this set.

{HTH}