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?
+128460 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
