a grab bag contains 20 packages worth $0.70 each 15 packages $0.60 each and five packages worth 30 cents each what is the expected value if you have to pay fifty cents each to pick one package at random​

The expected value is $0.1125

Step-by-step explanation:

The number of packages worth $0.70 in the grab bag = 20

The number of packages worth $0.60 in the grab bag = 15

The number of packages worth 30 cents in the grab bag = 5

The amount paid to pick one package = 50 cents

The number of packages in the bag, n = 20 + 15 + 5 = 40

The total value of the packages in the grab bag, 'V', is given as follows;

V = 20 × $0.70 + 15 × $0.60 + 5 × $0.30 =  $24.5

The average value of the packages in the bag, A = V/n

∴ A = $24.5/40 = 0.6125

The expected value is the value of the investment, at a point in time, the expected value E(X) is found by finding the sum of the of the calculations of the possible outcomes as follows

Whereby a $0.70 package is picked up, we have;

E(X)₁ = ($0.70 - $0.50) × 20/40 = $0.10

Whereby a $0.60 package is selected, we have;

E(X)₂ = ($0.60 - $0.50) × 15/40 = $0.0375

Whereby a $0.30 package is selected, we have;

E(X)₃ = ($0.30 - $0.50) × 5/40 = $(0.025)

Therefore, the expected value, E(X), is found as follows;

E(X) = E(X)₁ + E(X)₂ + E(X)₃

E(X) = 0.1 + 0.0375 - 0.025 = $0.1125

The expected value, E(X) = $0.1125

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