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Math algebra 2 help

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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?

Apr 15, 2019

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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

Apr 15, 2019