Question

An investor is interested in purchasing an apartment building containing six apartments. The current owner provides the following probability distribution indicating the probability that the given number of apartments will be rented during a given month.

Number of Rented Apartments	0	1	2	3	4	5	6
Probability	7⁄36	1⁄18	1⁄9	1⁄4	1⁄12	5⁄18	1⁄36

Find the number of apartments the investor could expect to be rented during a given month. (Hint: Find the expected value.)

a) 2.9667

b) 2.9167

c) 2.9367

d) 2.9067

e) 2.8767

2. The odds that a child entering a convenience store with her parents will not get a package of cupcakes are 1 to 13. What is the probability she will get a package of cupcakes?

a) 0.0714

b) 0.1494

c) 0.0769

d) 0.0115

e) 0.9286

f) None of the above.

Answer 1

a)

The expected number of rented apartments =

= 0 * (7/36) + 1 * (1/18) + 2 * (1/9) + 3 * (1/4) + 4 * (1/12) + 5 * (5/18) + 6 * (1/36)

= 2.916667

So, b) 2.9167 is the correct answer.

2.

The odds that a child entering a convenience store with her parents will not get a package of cupcakes are 1 to 13.

So, the probability she will not get a package of cupcakes = 1 / (1 + 13) = 1/14

The probability she will get a package of cupcakes = 1 - (1/14) = 13/14 = 0.9285714

So, the correct answer is e) 0.9286