UP - Expected Allowance Lesson

Expected Allowance 

cashYvonne gets $15 a week for allowance. She also loves to play basketball. Yvonne wants to convince her father to try something new with her allowance based on her basket-shooting talent, hoping that it will increase what she receives. Yvonne suggests that instead of getting $15, she shoots baskets each week for her allowance.

  • If she misses the first basket, she gets only $5.
  • If she makes the first basket, she gets $15 and a chance to make another basket for an additional $10.
  • **Yvonne can make a basket 40% of the time.

To help Yvonne's father decide whether to use the new allowance plan, find the probability of Yvonne making 0 baskets, I basket, and 2 baskets. Since Yvonne can make 40% of her baskets, you also know that she misses 60% of the time.

 

So the probability of 1 basket is 40% or 0.40 and the probability of missing 1 basket is 60% or 0.60. 

P(H)=(0.40)

P(M)=(0.60)

 

What is the probability of making 2 baskets and earning $25?

P(2H)=(0.40)(0.40) = 0.16 or 16%

P($25) = 0.16

 

What is the probability of making the first basket and missing the second, earning $15?

P(HM) = (0.40)(0.60)=0.24 or 24%

P($15) = 0.24

 

What is the probability of missing the first basket and only earning $5?

P(M) = 0.60 = 60%

P($5) = 0.60 

 

Using the area model, the purple shaded area represents missing the basket 60% of the time, and the blue shaded area represents making the basket 40% of the time. Out of the 40% category, she has a 40% chance of making another basket.

Area Model

basketball

Question #1 - How many times in a year do you expect Yvonne to get $5? $15? $25?

If you consider that there are 52 weeks in a year, then:

60% of the time Yvonne gets $5

0.60 x 52 = 31.2

So, for 31 weeks, she expects $5

 

24% of the time, Yvonne gets $15

0.24 x 52 = 12.5

So, for 13 weeks, she expects $15

 

16% of the time, Yvonne gets $25

0.16.52 = 8.3

So, for 8 weeks, she expects $25

Question #2 - How much allowance would she receive in total?

question 2 equation allowance

Question #3 - Should Yvonne's father accept the deal? Justify your reasoning.

Under the old deal, her father paid her $15 per week.

$15 x $52 = $780

Under the new deal, he can expect to pay her only $550.

He should take the deal!

Self-Assessment: Basketball Allowance

Yvonne practiced shooting baskets all year. She can now make a basket 60% of the time. Yvonne offers her father the same deal.

Follow the above example as a guide and determine whether her father should still make the deal. Be sure to make an area model with the new data.

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