Question

A student is choosing which classes to take in the spring. She chooses math with probability 5/8 and Spanish with probability 5/8 and neither math nor Spanish with probability 1/4. What's the probability that she chooses both math and Spanish?

Answer 1

0.5 is the probability that the student chooses both math and Spanish.

Explanation:

We are given the following in the question:

M: Math class

S: Spanish class

`P(M) = (5)/(8)\\\\P(S) =(5)/(8)\\\\P(M'\cap S') = (1)/(4)`

We have to evaluate the probability that she chooses both math and Spanish.

According to De-Morgans law

`P(M\cup S)' = P(M'\cap S')\\\\P(M\cup S)' = (1)/(4)\\\\P(M\cup S) = 1 - P(M\cup S)' = 1 - (1)/(4) = (3)/(4)`

Now, using the relation:

`P(M\cup S) = P(M) + P(S) - P(M\cap S)\\\\\displaystyle(3)/(4) = (5)/(8) + (5)/(8) - P(M\cap S)\\\\P(M\cap S) = (1)/(2) = 0.5`

Thus, 0.5 is the probability that the student chooses both math and Spanish.