Question

At a large high school, the favorite colleges for students to go on to are Floral College, Expanding University, Disco Tech, and Reform Institute. Of the students who go to one of these, 40% go to Floral, 25% to Expanding, 20% to Disco, and 15% to reform. According to the records of those colleges, 75% of Floral entrants graduate, 60% of Expanding entrants graduate, 80% of Disco entrants graduate, and only 40% of Reform entrants graduate.

a)A student from this high school will be going to one of these favorite colleges, but you do not know which one. What is the probability that student will graduate from the college chosen?

b)A few years later in a Bigbucks coffee shop you meet a student from this high school who entered one of the favorite colleges. She tells you she dropped out. What is the probability she went to Expanding University?

Answer 1

a)

Required probability = P(student graduates from the chosen college)

= P(student graduates from Floral) + P(student graduates from Expanding) + P(student graduates from Disco) + P(student graduates from Reform)

=

b)

Required probability = P(student went to Expanding | student dropped out)

= P(student went to Expanding and student dropped out) / P(student dropped out)

Now,

P(student drops out)

= P(student drops out from Floral) + P(student drops out from Expanding) + P(student drops out from Disco) + P(student drops out from Reform)

=

Required probability =