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
[tex]P(M) = \dfrac{5}{8}\\\\P(S) =\dfrac{5}{8}\\\\P(M'\cap S') = \dfrac{1}{4}[/tex]
We have to evaluate the probability that she chooses both math and Spanish.
According to De-Morgans law
[tex]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}[/tex]
Now, using the relation:
[tex]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[/tex]
Thus, 0.5 is the probability that the student chooses both math and Spanish.
