+0  
 
0
145
1
avatar

Danielle 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, 4, 4, and 5. If the sum of the two spins is greater than 6, Danielle is awarded $8. Otherwise, she must pay $2.

OPTION B: Flip a coin three times. If heads appears once, Danielle is awarded $6. Otherwise, she must pay $1.

Danielle chooses the option with the greater mathematical expectation.

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

 May 7, 2019
 #1
avatar+106533 
+1

Option A.....we have the following possible outcomes

(1,1)   (1, 5)     (4,5)

(1,4)    (5, 1)    (5,4)

(4,1)     (4, 4)   (5, 5)

 

4 of the 9 outcomes have a sum > 6....and 5 don't

So....expected value  =  (4/9)(8) - (5/9)(2)  ≈ $2.44

 

Option B

We have 8 possible outcomes.....only 3 of them have heads appearing once

So....expected value  =  (3/8)(6)- (5/8)(1)  ≈ $1.63

 

"B" is better by ≈  $[ 2.44 - 1.63 ]  =  81 cents

 

cool cool cool

 May 7, 2019

9 Online Users