The expected earnings are the probability of drawing each type of bead with their respective earnings.
Expected value: $1.83 Is it a fair game?: No.
Practice makes perfect
Let's start by illustrating the problem.
If we multiply the probability of drawing each type of colored bead by their respective earnings, the sum of these values should equal 0 for it to be a fair game. Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
With this information we can identify the probability of drawing each type of bead.
P(blue)&=7/12 [0.8em]
P(red)&=3/12 [0.8em]
P(yellow)&=2/12
Now we can calculate the expected earnings from each type of bead.
Event
P
Earnings
P * Earnings
Expected Earnings ($)
P(blue)
7/12
- 1
7/12( - 1)
- 7/12
P(red)
3/12
3
3/12( 3)
9/12
P(yellow)
2/12
10
2/12( 10)
20/12
By adding all of the expected earnings, we can get the average earnings.
