Rational decisions

Question 1

After watching the quiz game video, How would you make the decision of quitting or guessing at random in a rational way

Answer 1

If you quit, you walk away with 100,000. If you guess and get it wrong, you get 62.000 and if guess correctly, you get 250,000. Therefore, you have a 1 in 4 chance of getting 250,000 and a 3 in 4 chance of getting 62,000.

Hence, in expectation, you would get 620000.75 + 2500000.25 = 109,000 if you randomly guess. This is 9000 more than what you would get if you quit!