Question

The probability that Mary will win a game is 0.03, so the probability that she will not win is 0.97. If Mary wins, she will be given $180; if she loses, she must pay $17. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)

Answer 1

Expected value of X = -11.09

Step-by-step explanation:

Expected profit:

= Probability of winning × Amount she wins

= 0.03 × $180

= 5.4

Expected loss:

= Probability of loosing × Amount she paid

= 0.97 × $17

= 16.49

Let X be amount of money Mary wins or loses.

E(X) = Expected profit - Expected loss

= 5.4 - 16.49

= -11.09

Expected value of X = -11.09

That is expected value of loss of $11.09