Question

On Mr. Casper’s debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85.

Answer 1

Answer:

here is a 63.25% for winning the debate given the student distribution and the chance of success  of each type of student.

Explanation:

As the student will be picked at random we can determiante the expected value by doing a weighted average:

$\left[\begin{array}{cccc} Student& Return& Probability& Weight\\ Sophomore&0.2&0.2&0.04\\ Junior&0.6&0.35&0.21\\ Senior&0.85&0.45&0.3825\\Total&&1&0.6325\\\end{array}\right]$