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Following is my assignment question.

Suppose that an experiment is performed on three courses being taught which are $C_1$, $C_2$ and $C_3$. The class of $C_1$ contains $30$ MS students, $40$ undergraduate students(U), and $10$ PhD students, class of $C_2$ contains $10$ MS , $10$ U, and $0$ PhD students, and class of $C_3$ contains $30$ MS, $30$ U, and $4$ PhD students If a class is chosen at random with probabilities $p(C_1) = 0.2, p(C_2) = 0.2, p(C_3) = 0.6$, and a student is chosen from the class (with equal probability of selecting any of the students in the class and each student is enrolled in only one course), then what is the probability of selecting an MS student? This is how I calculated the answer but I am not sure whether it is correct or not.

$$\left(\frac{30}{80} \times 0.2\right)+\left(\frac{10}{20} \times 0.2\right)+ \left(\frac{30}{64} \times 0.6\right)=0.45$$

Please tell if I have solved this correctly.

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    $\begingroup$ Why is this being down-voted? The OP did the calculation and now wants confirmation that it is correct. S/he is not asking us to do his/her homework $\endgroup$
    – mdewey
    Oct 18, 2017 at 8:45

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The approach is correct.

You are using the law of total probability:

$$\Pr(\text{Ms})= \sum_{i=1}^3 Pr(\text{Ms}|C_i)Pr(C_i)$$

of which upon evaluating gives us $\approx 0.45625$

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