A multiple choice test contains 12 questions, 8 of which have 4 answers each to choose from and 4 of which have 5 answers to choose from. If a student randomly guesses all of his answers, what is the probability that he will get exactly 2 of the 4 answer questions correct and at least 3 of the 5 answer questions correct?(adsbygoogle = window.adsbygoogle || []).push({});

ANS: 0.2552

Heres what I did:

Out of the 8-four answer questions, the student gets 2 of them = (8C2)

Out of the 4-five answer questions, the student gets 3 of them = (4C3)

Therefore:

[8C2(.25)^2(.75)^6][ 4C3(.2)^3(.8)^1+ 4C4(.2)^4(.8)^0].

So:

The probability of getting exactly two of the eight four-option questions is 0.31146240234375.

The probability of getting at least three of the four five-option questions is 0.0272.

Those two are clearly independent. The product of those probabilities is 0.00847177734375.

BUT...the answer is suppose to be 0.2552 apparently.

Any input?

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# Discrete random variables

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