P - 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. Check your answers with the key.

Answer Key Links to an external site.

 

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