(Find the expected value of the winnings from a game that has the following payout probability) I have all the answers with work shown and how to solve on the second image
Hope this help you guys :)

The expected value is $2.1

Step-by-step explanation:

If we have an event with some given outcomes:

x₁, x₂, ..., xₙ

Such that each one of these outcomes has the correspondent probability:

p₁, p₂, ..., pₙ

The expected value is:

EV = p₁*x₁ + ... + pₙ*xₙ

In this case we have a table with the events (the payouts) and the probability for each one, so we have:

x₁ = $0

p₁ = 0.5

x₂ = $2

p₂ = 0.2

x₃ = $4

p₃ = 0.15

x₄ = $6

p₄ = 0.1

x₅ = $10

p₅ = 0.05

Now we can just replace these in the expected value equation, so we get:

EV = $0*0.5 + $2*0.2 + $4*0.15 + $6*0.1 + $10*0.05 = $2.1

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5