John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year.

Number of Lease Offices 0 1 2 3 4 5
Probability 10/33 1/33 7/33 1/11 4/33 8/33
If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)
a) E(X) = $29,130.91
b) E(X) = $29,090.91
c) E(X) = $29,170.91
d) E(X) = $29,070.91
e) E(X) = $29,100.91

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The given table is:

Number of Lease Offices : 0 1 2 3 4 5

Probability : 5/18 1/4 1/9 1/18 2/9 1/12

The expected probability is

Expected probability [tex]$=\sum_{i=0}^5 x_i p\left(x_i\right)$[/tex]

Expected probability [tex]$=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$[/tex]

Expected probability [tex]$=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$[/tex]

It is given that the yearly lease [tex]$=\$ 12,000$[/tex].

The yearly leases for the whole building in a given year is

Yearly leases [tex]$=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$[/tex]

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