# Calculate Expectation : $150$ questions each with $4$ options

In exam , there are $150$ questions each with $4$ options

for each correct response $+1$ mark is awarded

for each incorrect response $-0.25$ mark is deducted

If $1000$ students appear for exam and all of them mark answers to all questions randomly

then Calculate Score expected by each student ..?

Ans : $\frac{150}{16}$

How...?

My approach : i created probability distribution table and then tried to calculate the ans using $E(x) =$ $\sum(x_iP(x_i) )$ which is a tiresome approach.

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The expected score for a single question is $\frac14\cdot (+1)+\frac34\cdot(-0.25)=\frac1{16}$. Since expected values add, the expected total score for one student is $\frac{150}{16}$.

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thank you.......:) –  Jay Satish Teli Feb 9 '13 at 9:20