Problem 1 Question B 50 meters swimming pool Team The Unive

Problem # 1, Question B)
50 meters swimming pool Team:

The University of Jaiba has a swim team that is very competitive in the 50 meters distance competition. Jaiba swimmers competing in the event are trained by one of three coaches, namely : Michael , Robert and Jose.

DATA:

According to The records, fractions of swimmers who are trained by these three trainers are:

Michael trains 30 % of the swimmers

Robert trains 20% of the swimmers

Jose trains 50% of the swimmers.

According to statistics from past competitions in the league:

- 5% of the swimmers trained by Michael have won the competition.

- 4% of the swimmers trained by Robert have won the competition.

- 6% of the swimmers trained by Jose have won the competition.

B) A swimming competition recently was held at a distance of 50 meters and the winner was an athlete at the University of Jaiba . What is the probability that the contestant who won was trained by Jose? (Define and identify with clarity the events under consideration and his respective probability).

Solution

A rough sketch of the tree is as follows:

Michael - 30% training - 5% winners

Robert - 20% - 4%

Jose - 50% - 6%

P(contestant won was trained by Jose) = P(contestant won and trained by JOse)/P(trained by Jose)

= 50(6)/{30(5)+20(4)+50(6) by Bayes prob

= 300/530 = 0.5661