Question

Two friends, Eric and Jason, take the probability midterm exam. They have equal probability of getting an A. The probability that at least one of them gets an A is 0.7 and both get an A is 0.3. What is the probability that Jason gets an A, and the probability that Eric gets an A given that Jason got an A?

Answer 1

Let E for Eric and J for Jason

P(E J) = 0.7 , P(E J) = 0.3

Using addition rule,

P(E J) = P(E) + P(J) - P(E J)

Since Eric and Jason have equal probability of getting an A, P(E) = P(J)  

P(E J) = P(J) + P(J) - P(E J)

0.7 = 2 P(J) - 0.3

2 P(J) = 1.0

P(J) = 0.5

Probability of Jason gets an A = 0.5

P(E | J) = ?

P(E | J) = P(E J) / P(J)

= 0.3 / 0.5

= 0.6

The probability that Eric gets an A given that Jason got an A = 0.6