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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?

 

I think it is $4.05

 May 1, 2019
 #1
avatar+102948 
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Option A.....possible outcomes

(1, 1)  (2, 2)

(1, 2)  ( 2,5)

(2, 1)   (5,2)

(1, 5)   (5, 5)

(5, 1)

 

Expected vlalue  = (3/9)(8)  - (6/9)(2)  =   8/3 - 4/3  ≈ $1.33

 

 

Option B

Expected value (50/((1/8) - (1)(7/8)  ≈ $5.38

 

Ptiob B is better by  $ [ 5.38 - 1.33]  =  $4.05

 

 

 

cool cool cool

 May 1, 2019

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