Question

Need help with well-explained solution

1. Assume that there are two urns. The first urn contains 4 red balls, 3 blue balls, and 3 white balls. The second urn contains 2 red balls, 4 blue balls, and 4 white balls. You randomly select an urn and take two balls from the urn. The probability that you pick the first urn is 40%. What is the probability that

(a) the two balls are red?

(b) the second ball is blue?

(c) the second ball is blue given that the first ball is red?

2. Generally, students who study regularly have a probability of 85% to get an A, 10% to get a B, and 5% to get a C or lower. Unfortunately, some students only study right before a test. These students have a probability of 50% to get an A, 15% to get a B, and 35% to get a C or lower. Thankfully, the students who study regularly make up 90% of the student body.

(a) Given that a student received an A on the test, what is the probability that they studied?

(b) Given that a student received a B or lower, what is the probability that they didn’t study?

Answer 1

Let A be the event that the first urn is picked then and  

Suppose the chosen balls are red

Let B be the event of choosing two red balls

Then

  

   ( Since there are 4 red balls in the first urn and 2 red balls in the second urn)

Let C be the event that the second ball is blue

Let D be the event that the second ball is blue given that the first ball is red

2)