Question

Suppose an urn contains 50 balls: 25 are red, the rest are either blue or green in unknown proportion. A random ball will be drawn, and you must choose one of the following.

• 1A: you win $5 if the ball is red,
• 1B: you win $5 if the ball is blue.

You also face a second choice:

• 2A: you win $5 if the ball is either blue or green,
• 2B: you win $5 if the ball is either red or green.

Which one of the following is correct?

Group of answer choices

A. None of the above.

B. Preferring 1B and 2A violates the sure-thing principle.

C. Preferring 1A and 2A violates the sure-thing principle.

D. Preferring 1B and 2A violates the axioms of probability.

Answer 1

Answer : Part ( C) Preferring 1A and 2A violates the sure-thing principle.
Reason: We are having 50 balls.
Outcomes are either red with a probability of 0.5 ( 25/50) and black or green together with a probability of 0.5(25/50)
Thus choosing option 1A and 2A says that we have expected amount :
0.5 ($5) + 0.5 ( $5) = $ 5 which is certain .
It violates the sure -thing principle which states that a decision maker would take a certain action if he knew that Event E can occur but he knows nothing about that event .
Here , the decision maker has surity that the will either be red or black or green .
Thus it is absurd to take this option choice and sure-thing principle will be violated .