Exercise 120 Page 526

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.

20/12+9/12+(- 7/12)

AddNeg

a+(- b)=a-b

20/12+9/12-7/12

AddSubFrac

Add and subtract fractions

22/12

CalcQuot

Calculate quotient

1.83333...

RoundDec

Round to 2 decimal place(s)

≈ 1.83

The expected earnings are $1.83, which means it is not a fair game. This means if you play long enough you are expected to win $1.83.