Question

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.

probability and milk cost by store
a	30%	$3.00
b	10%	$3.50
c	60%	$2.75

the cafeteria should budget $<select>
2.88
2.90
3.00
3.08</select> on average for one gallon of milk.

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:

$2.90$