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}
. The slope is -3/2. The slope of a line that is perpendicular to line k will have the opposite sign (so, positive) and will be the reciprocal of the line k's slope (so, 2/3). You could also say, more "mathematically legal", that the product of the slopes of perpendicular lines is -1, but it's easier to just say that they are opposite reciprocals. The slope you're looking for is 2/3. Choice 3 above.