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Anya may choose one of two options for the method in which she may be awarded a money prize. 

OPTION A: Spin a spinner twice. The spinner is divided into four equally-sized sectors numbered 1, 2, 5, and 5. If the sum of the two spins is greater than 6, Anya is awarded $8. Otherwise, she must pay $2. 

OPTION B: Flip a coin three times. If heads appears 3 times, Anya is awarded $50. Otherwise, she must pay $1. 

Anya chooses the option with the greater mathematical expectation. 

How much more money can Anya expect to make by choosing this option over the other option?

 Apr 15, 2019
 #1
avatar+101870 
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Option A        ( 1, 2 , 5 , 5)

We have  these possible outcomes on two spins

(1, 1) ( 1,2) (2,1) (2,2) (1,5) (5,1) (2,5) (5,2) (5,5)

We have 3 outcomes whose sums are > 6  

So....the expected value is

$8(3/9) - $2(6/9) =

$ ( 8/3 - 4/3) =

$ (4/3) ≈  $1.33

 

Option B

We have 2^3  = 8 possible outcomes

Only one of these is 3 heads

So...the expected value is

$50(1/8) - $1(7/8) =

$ ( 50 - 7 ) / 8 =

$(43)/8 ≈ $5.38

 

Option B   is much better by   ≈  $ ( 5.38 - 1.33)  ≈ $ 4.05

 

 

cool cool cool

 Apr 15, 2019

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