SOLUTION: The probability that Mary will win a game is 0.02, so the probability that she will not win is 0.98. If Mary wins, she will be given $200; if she loses, she must pay $18. If X = am

Algebra ->  Probability-and-statistics -> SOLUTION: The probability that Mary will win a game is 0.02, so the probability that she will not win is 0.98. If Mary wins, she will be given $200; if she loses, she must pay $18. If X = am      Log On


   

Question 867113: The probability that Mary will win a game is 0.02, so the probability that she will not win is 0.98. If Mary wins, she will be given $200; if she loses, she must pay $18. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
E[X] = (Probability of Winning)*(Value of Winning) + (Probability of Losing)*(Value of Losing)


E[X] = (0.02)*(200) + (0.98)*(-18)


E[X] = (4) + (-17.64)


E[X] = -13.64


Her expected value is -13.64 dollars


So she expects to lose $13.64 every time she plays (this is on average).