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.

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

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) = $\frac{94}{208} + \frac{106}{208} = \frac{200}{208} = \frac{25}{26}$
P(NOT A) = $1- \frac{25}{26} = \frac{1}{26}$
P(B and NOT A) = P(males that did not choose cat or dog) = $\frac{6}{208} = \frac{3}{104}$

P(B | NOT A) = $\frac{P(B \, and \, NOT \, A)}{P(NOT \, A)} = \frac{ \frac{3}{104} }{ \frac{1}{26} } =\frac{3}{104}\times26= \frac{3}{4}$


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
$\ 20.90\times0.3+(-\ 19\times0.7)=\ 6.27-\ 13.30=-\ 7.03$

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