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.

store	probability	milk cost per gallon
b	10%	$3.50
c	60%	$2.75

the cafeteria should budget $ on average for one gallon of milk.

Explanation:

Step1: Recall expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i}p_ix_i$, where $p_i$ is the probability of the $i$ - th outcome and $x_i$ is the value associated with the $i$ - th outcome.

Step2: Identify values for each store

For store A: $p_A = 0.3$ and $x_A=3.00$; for store B: $p_B = 0.1$ and $x_B = 3.50$; for store C: $p_C=0.6$ and $x_C = 2.75$.

Step3: Calculate the expected value

$E(X)=p_Ax_A + p_Bx_B + p_Cx_C$
$E(X)=0.3\times3.00+0.1\times3.50 + 0.6\times2.75$
$E(X)=0.9+0.35 + 1.65$
$E(X)=2.90$

Answer:

$2.90$