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 neithe

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?

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Gianna 2 weeks 2022-01-08T06:59:02+00:00 1 Answer 0 views 0

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    2022-01-08T07:00:08+00:00

    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.

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45:7+7-4:2-5:5*4+35:2 =? ( )