Question

a cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchas the probability of shopping at each store and the cost of one gallon of milk are shown in the table below
probability and milk cost by store
store | probability | milk cost per gallon
a | 30% | $3.00
b | 10% | $3.50
c | 60% | $2.75
the cafeteria should budget $dropdown on average for one gallon of milk.
dropdown options: 2.88, 2.90, 3.00, 3.08

Explanation:

Step1: Recall the formula for expected value

The expected value \( E(X) \) of a discrete random variable is calculated as \( E(X)=\sum_{i} x_i P(x_i) \), where \( x_i \) is the value of the random variable and \( P(x_i) \) is the probability of \( x_i \).

Step2: Convert probabilities to decimals

• For Store A: Probability \( P_A = 0.3 \), Cost \( x_A = 3.00 \)
• For Store B: Probability \( P_B = 0.1 \), Cost \( x_B = 3.50 \)
• For Store C: Probability \( P_C = 0.6 \), Cost \( x_C = 2.75 \)

Step3: Calculate the expected value

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Answer:

2.90