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?

Guest May 7, 2019

#1**+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

CPhill May 7, 2019