a cafeteria purchases milk from one of three providers each week, depending on what other items need to be…

a cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. the probability of shopping at each store and the cost of one gallon of milk are shown in the table below.\n\n| probability and milk cost by store | | |\n|--|--|--|\n| store | probability | milk cost per gallon |\n| a | 30% | $3.00 |\n| b | 10% | $3.50 |\n| c | 60% | $2.75 |\n\nthe cafeteria should budget $<select>\n2.88\n2.90\n3.00\n3.08</select> on average for one gallon of milk.

a cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. the probability of shopping at each store and the cost of one gallon of milk are shown in the table below.\n\n| probability and milk cost by store | | |\n|--|--|--|\n| store | probability | milk cost per gallon |\n| a | 30% | $3.00 |\n| b | 10% | $3.50 |\n| c | 60% | $2.75 |\n\nthe cafeteria should budget $<select>\n2.88\n2.90\n3.00\n3.08</select> on average for one gallon of milk.

Answer

Explanation:

Step1: Convert probabilities to decimals

$P(A)=0.3$, $P(B) = 0.1$, $P(C)=0.6$

Step2: Use expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i}x_ip_i$. Here, $x_A = 3.00$, $x_B=3.50$, $x_C = 2.75$. So $E(X)=3.00\times0.3 + 3.50\times0.1+2.75\times0.6$.

Step3: Calculate each product

$3.00\times0.3=0.90$, $3.50\times0.1 = 0.35$, $2.75\times0.6=1.65$.

Step4: Sum up the products

$E(X)=0.90 + 0.35+1.65=2.90$.

Answer:

$2.90$