To solve this, let's go step-by-step through the information provided and determine the probability that Jamie will be selected as the third player.
1. Understand the given scenario:
- Coach Bennet selects one senior and one junior as the first two players.
- Taylor and Jamie are both juniors on the team.
- Taylor is selected as one of the first two players.
2. Determine the total number of juniors and seniors on the team:
- Let's denote the number of juniors by [tex]\( J \)[/tex] and the number of seniors by [tex]\( S \)[/tex]. We need the context or prior knowledge to specify these.
- For this solution, let's assume that each, [tex]\( J \)[/tex] and [tex]\( S \)[/tex], is 10, making [tex]\( J = 10 \)[/tex] and [tex]\( S = 10 \)[/tex].
3. Exclude Taylor, who has already been selected:
- Since Taylor is already selected, he is out of the pool of remaining players. Thus, the remaining juniors are [tex]\( J - 1 = 10 - 1 = 9 \)[/tex].
4. Calculate the total number of remaining players:
- The total number of remaining players after selecting Taylor is the sum of juniors (excluding Taylor) and the seniors:
[tex]\[
\text{Total remaining players} = (J - 1) + S = 9 + 10 = 19
\][/tex]
5. Calculate the probability of selecting Jamie as the third player:
- Since the coach randomly selects the third player from any of the remaining players, the probability of selecting Jamie (who is one specific player out of the 19 remaining) is:
[tex]\[
\text{Probability} = \frac{1}{\text{Total remaining players}} = \frac{1}{19}
\][/tex]
6. Convert the probability to a decimal format:
- The probability in decimal form is:
[tex]\[
0.05263157894736842
\][/tex]
Given the conditions and the steps above, the probability that Jamie will be selected as the third player, given that Taylor is already one of the first two players selected, is [tex]\( 0.05263157894736842 \)[/tex].
