Expected value question

Question

Kevin is playing a carnival game where he draws a marble from a bag. Each color is worth a different dollar value: purple marble wins $1, red marble wins $5, green marbles wins $20, and orange marble wins $100. The bag has 70 purple marbles, 25 red marbles, 4 green marbles, and 2 orange marbles. Every time a marble is drawn, it is replaced with the same colored marble.

What is the expected value for a single draw? Make sure to type your answer as $0.00 (with two decimals) If the expected value is negative, type your answer as -$0.00 (with two decimals).

Answer 1

let x be winnings, P(x) be probability of winning

marble color x P(x)

purple 1 70/101

red 5 25/101

green 20 4/101

orange 100 2/101

expected value is sum of x*P(x)