Rachel plays a game where she can randomly select 1 of 3
cards. If she selects Card A, she will win $10. If she selects Card B, she will win $15. If she selects card C, she will win $50.
What is the expected value of winning?
To calculate the expected value of winning, we need to multiply the value of each prize by the probability of winning that prize and then sum up these values.
The probability of selecting Card A is 1/3, so the expected value of winning with Card A is:
(1/3) * $10 = $3.33
The probability of selecting Card B is also 1/3, so the expected value of winning with Card B is:
(1/3) * $15 = $5
The probability of selecting Card C is again 1/3, so the expected value of winning with Card C is:
(1/3) * $50 = $16.67
Adding up these three expected values gives us the total expected value of winning:
3.33 + 5 + 16.67 = $25
Therefore, the expected value of winning in this game is $25.