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I have some conceptual hiccups ( for a lack of better word ) with beta Random variables.

Here's the question:

The number of students who get failing grade in a hard test is given by Beta B(2,3) random variable.

α = 2, β= 3

To determine the number of students that fail, I found the Mode using the formula Mode = (α−1)/(α+β−2)

I get (2-1)/(2+3-2) = 1/3

Therefore, the number of students that fail is 1/3rd.

Is this right?

Now how do I find the the probability of 80% students passing the test?

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