Question

Please help me with this

Answer 1

Answer:

The expected value of the guess is:

                            -0.125

Step-by-step explanation:

We know that for each answer there is one correct choice and 3 incorrect choice.

Hence,

$P(correct\ answer)=\dfrac{1}{4}$

and

$P(incorrect\ answer)=\dfrac{3}{4}$

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:

$Expected\ Value=P(correct\ answer)\times 1+P(incorrect\ answer)\times (-0.5)\\\\i.e.\\\\Expected\ Value=\dfrac{1}{4}+\dfrac{3}{4}\times (-0.5)\\\\i.e.\\\\Expected\ Value=\dfrac{1}{4}-\dfrac{1.5}{4}\\\\i.e.\\\\Expected\ Value=\dfrac{-0.5}{4}\\\\i.e.\\\\Expected\ Value=-0.125$

Answer 2

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