You question is of two parts.
For the first part:
<span>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}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%0A%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0A%20%26%20Cats%20%26%20Dogs%20%26%20Other%20%26%20Total%20%5C%5C%20%5B1ex%5D%0AMale%20%26%2042%20%26%2058%20%26%206%20%26%20106%20%5C%5C%0AFemale%20%26%2052%20%26%2048%20%26%202%20%26%20102%20%5C%5C%20%5B1ex%5D%0ATotal%20%26%2094%20%26%20106%20%26%208%20%26%20208%0A%5Cend%7Btabular%7D%0A%5Cend%7Bcenter%7D)
</span>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}](https://tex.z-dn.net/?f=%20%5Cfrac%7B94%7D%7B208%7D%20%2B%20%5Cfrac%7B106%7D%7B208%7D%20%3D%20%5Cfrac%7B200%7D%7B208%7D%20%3D%20%5Cfrac%7B25%7D%7B26%7D)
P(NOT A) =
![1- \frac{25}{26} = \frac{1}{26}](https://tex.z-dn.net/?f=1-%20%5Cfrac%7B25%7D%7B26%7D%20%3D%20%5Cfrac%7B1%7D%7B26%7D%20)
P(B and NOT A) = P(males that did not choose cat or dog) =
![\frac{6}{208} = \frac{3}{104}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B208%7D%20%3D%20%5Cfrac%7B3%7D%7B104%7D%20)
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}](https://tex.z-dn.net/?f=%20%5Cfrac%7BP%28B%20%5C%2C%20and%20%5C%2C%20NOT%20%5C%2C%20A%29%7D%7BP%28NOT%20%5C%2C%20A%29%7D%20%3D%20%5Cfrac%7B%20%5Cfrac%7B3%7D%7B104%7D%20%7D%7B%20%5Cfrac%7B1%7D%7B26%7D%20%7D%20%3D%5Cfrac%7B3%7D%7B104%7D%5Ctimes26%3D%20%5Cfrac%7B3%7D%7B4%7D%20)
For the second part of the question.
<span>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](https://tex.z-dn.net/?f=%5C%2420.90%5Ctimes0.3%2B%28-%5C%2419%5Ctimes0.7%29%3D%5C%246.27-%5C%2413.30%3D-%5C%247.03)
Therefore, Petey should not make the investment as there is an expectation of a loss from the investment.
</span>