Question

A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.

Answer 1

You question is of two parts.
For the first part:
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.


`\begin{center} \begin{tabular} c & Cats & Dogs & Other & Total \\ [1ex] Male & 42 & 58 & 6 & 106 \\ Female & 52 & 48 & 2 & 102 \\ [1ex] Total & 94 & 106 & 8 & 208 \end{tabular} \end{center}`

Let event A be defined as randomly choosing someone who picked cats or dogs as their favorite pet. Let event B be defined as a randomly chosen person being male.
Find P(B| NOT A).

P(A) = P(choosing cat) + P(choosing dog) =
`(94)/(208) + (106)/(208) = (200)/(208) = (25)/(26)`
P(NOT A) =
`1- (25)/(26) = (1)/(26)`
P(B and NOT A) = P(males that did not choose cat or dog) =
`(6)/(208) = (3)/(104)`

P(B | NOT A) =
`(P(B \, and \, NOT \, A))/(P(NOT \, A)) = ( (3)/(104) )/( (1)/(26) ) =(3)/(104)*26= (3)/(4)`


For the second part of the question.
Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.

If his investment increases by 10%, the value of the investment will be 1.1 x $19 = $20.90 with a probability of 30% or 0.3

The expected value of the investment is given by

`\$20.90*0.3+(-\$19*0.7)=\$6.27-\$13.30=-\$7.03`

Therefore, Petey should not make the investment as there is an expectation of a loss from the investment.