Question

suppose coach bennet selects one senior and one junior as the first two players. the coach then randomly selects the third player from either group. taylor and jamie are both juniors on the team. if taylor is selected as one of the first two players, what is the probability that jamie will be selected as the third player? type in the correct answer in the box. use numerals instead of words. if necessary, round your answer to the nearest tenth. the probability that jamie will be selected as the third player, given that taylor is selected as one of the first two players, is %

Explanation:

Step1: Determine total remaining players

After the first - two players (one senior and one junior) are selected and Taylor is one of the first - two players, the number of remaining players is the total number of juniors and seniors minus 2. Since Taylor and Jamie are juniors, and we know the first two are a senior and a junior (with Taylor being one of them), there is 1 junior (Jamie) and some number of non - selected seniors. The total number of remaining players for the third - player selection is 1 (Jamie) + number of non - selected seniors. But in terms of the relevant player for our probability (Jamie), considering the selection of the third player from the remaining pool, there is 1 favorable outcome (selecting Jamie) and assume there are a total of 1 + n (where n is the number of non - selected seniors) remaining players. In the most basic sense, if we just consider the fact that we are choosing 1 player out of the remaining players for the third selection, and we are interested in Jamie being selected. After the first two players are chosen (with Taylor among them), there is 1 remaining junior (Jamie) and assume the number of remaining players is 1 (Jamie)+ other non - junior players. The probability of an event E (selecting Jamie as the third player) is given by the formula \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes is 1 (selecting Jamie) and assume the total number of remaining players is 2 (if we consider only the relevant situation where we are choosing between Jamie and one other non - junior player for simplicity, since we are only interested in the probability of choosing Jamie). So the probability \(P=\frac{1}{2}=0.5\) or 50%.

Answer:

50