Question

Determine (Freshman) Small Cafeteria). Interpret this answer in the context of the situation.

Answer 1

Step 1:

`\text{Probability = }\frac{N\text{umber of required outcomes}}{N\text{umber of total possible outcome}}`

Step 2:

a)

Total possible outcome = 2640

Total number of freshman = 625

`\begin{gathered} P(\text{Freshman) = }(625)/(2640) \\ \text{= }(125)/(528) \\ \text{= 0.237} \end{gathered}`

Step 3:

b)

Total number of senior and large cafeteria = 350

`\begin{gathered} P(\text{senior and large cafeteria) = }(350)/(2640) \\ =\text{ }(70)/(528) \\ =\text{ }(35)/(264) \\ =\text{ 0.132} \end{gathered}`

Step 4:

c)

Number of Sophomore or student center = 650 + 595 - 125 = 1120

`\begin{gathered} P(\text{Sophomore or student center) = }(1120)/(2640) \\ =\text{ }(112)/(264) \\ =\text{ 0}.424 \end{gathered}`

Step 5:

d)

`\begin{gathered} p(\text{freshman}|\text{small cafeteria) = }\frac{n(freahman\text{ and small cafeteria)}}{n(small\text{cafeteria)}} \\ =(435)/(860)\text{ } \\ =\text{ }(87)/(172) \\ =\text{ 0.506} \end{gathered}`