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?
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