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

Answer:

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

Step-by-step explanation:

We are given the following in the question:

M: Math class

S: Spanish class

$P(M) = \dfrac{5}{8}\\\\P(S) =\dfrac{5}{8}\\\\P(M'\cap S') = \dfrac{1}{4}$

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

According to De-Morgans law

$P(M\cup S)' = P(M'\cap S')\\\\P(M\cup S)' = \dfrac{1}{4}\\\\P(M\cup S) = 1 - P(M\cup S)' = 1 - \dfrac{1}{4} = \dfrac{3}{4}$

Now, using the relation:

$P(M\cup S) = P(M) + P(S) - P(M\cap S)\\\\\displaystyle\frac{3}{4} = \frac{5}{8} + \frac{5}{8} - P(M\cap S)\\\\P(M\cap S) = \frac{1}{2} = 0.5$

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