Prob ( guessing right) = 0.25 . Get 1 point.
Prob( guessing wrong) = 0.75. Lose 0.5 points.
Expected value = 1(0.25) + (-0.5)(0.75)
= -0.125 answer
The expected value of the guess is:
-0.125
We know that for each answer there is one correct choice and 3 incorrect choice.
Hence,
[tex]P(correct\ answer)=\dfrac{1}{4}[/tex]
and
[tex]P(incorrect\ answer)=\dfrac{3}{4}[/tex]
Also, 1 point is awarded for each correct response and 0.5 is deducted for each incorrect response.
Hence, the expected value of the guess is calculated by:
[tex]Expected\ Value=P(correct\ answer)\times 1+P(incorrect\ answer)\times (-0.5)\\\\i.e.\\\\Expected\ Value=\dfrac{1}{4}+\dfrac{3}{4}\times (-0.5)\\\\i.e.\\\\Expected\ Value=\dfrac{1}{4}-\dfrac{1.5}{4}\\\\i.e.\\\\Expected\ Value=\dfrac{-0.5}{4}\\\\i.e.\\\\Expected\ Value=-0.125[/tex]
