Expected Value: Marbles

Calculate expected value for marble scenarios

Calculator Dice Coins Marbles Cards Learn

Expected Red CountCount Prize DrawPrize Sequential ValueSequential

Expected Prize Value

$100

$20

The Game

A bag contains 2 red ($100 prize), 3 blue ($20 prize), and 5 white ($0) marbles. You draw one marble. What is your expected prize?

Step-by-Step Solution

List Outcomes and Probabilities

Color	Count	Prize (x)
Red	2	$100
Blue	3	$20
White	5	$0

Calculate Expected Value

Answer

E(Prize) = $26

On average, you win $26 per draw.

Is It Worth Playing?

If the game costs $C to play:

Cost < $26

Play!

Positive expected profit

Cost = $26

Fair

Break even on average

Cost > $26

Skip!

Expected loss

Key Insight

Expected value helps evaluate games even when prizes vary. The expected prize of $26 is close to the $20 blue prize because half the marbles (white) give $0, while only 20% give the big prize.