Question

You have won a game and can now choose between two options: option A: a gift of $10, guaranteed option B: a chance to keep playing to win $8000 with a probability of 0.001, otherwise winning only $2 (a consolation prize for having passed up the $10). Choosing option A has an expectation of $10. What is the expectation of option B

Answer 1

Answer:

$10

Explanation:

Lets assume we choice or go for option B, we will have a 0.999 probability of winning $2, and also we will have 0.001 probability of winning the $800. This is to say, expectation value B will be given as;

E(B) = 0.999×2+0.001×800

E(B) = $9.80

By approximating, we have expectation of B to be $10

Answer 2

Answer:

$10

Explanation:

By choosing option B, you have a 0.001 chance of winning $8000, and a 0.999 chance of winning the $2 consolation prize. Therefore, the expected value of option B is given by:

$E(B) = 0.001*\ 8000+0.999*\ 2\\E(B)=\ 9.998$

Rounding to the nearest cent, the expectation of option B is also $10.