Bayes theroem hw

[paola.zaragoza]

1)an advertising excecutive is studying tv viewing habits of married men and women.
husband watching tv 60%
husband and wife watch tv 40%
husband not watching tv and wife is watching tv 30%
find if wife is watching tv the husband is also watching tv
and the wife is watching tv
2)municipal bonds have 3 categories A, B, and Cthe past year there was
70% A 20% B and 10% C
A is composed of: 50% city, 40% suburbs and 10% rural
B is composed of: 60% city, 20% suburbs and 20% rural
C is composed of: 90% city, 5% suburbs and 5% rural
if a new bond is to be issued in a city what is the probability of it bieng ranked A
what proportion of bonds are issued in the city and in the suburbs (separately)

 

[soroban]

Hello, paola.zaragoza!

1) An advertising excecutive is studying tv viewing habits of married men and women.
. . Husband watching TV: 60%
. . Husband and Wife watch TV: 40%
. . Husband not watching TV and wife is watching TV: 30%

Find if wife is watching TV, the husband is also watching TV.

\(\displaystyle \text{We want: }\;P(\text{H watches }|\text{ W watches}) \;=\;\frac{P(\text{H watches }\wedge\text{ W watches})} {(\text{W watches})}\)


\(\displaystyle \text{The numerator is: }\(\text{H and W watches}) \:=\:40\%\)


\(\displaystyle \text{For the denominator, we can use a Venn diagram.}\)

\(\displaystyle \text{Using the given information, we have:}\)

      * - - - - - - - - - - - - - - - - - - - - - *
      |                                           |
      |       * - - - - - - - - - *               |
      |       | Husband only      |               |
      |       |  20%  * - - - - - + - - - *       |
      |       |       |    Both   |       |       |
      |       |       |     40%   |       |       |
      |       * - - - + - - - - - *       |       |
      |               |              30%  |       |
      |               |         Wife only |       |
      |      10%      * - - - - - - - - - *       |
      |   Neither                                 |
      * - - - - - - - - - - - - - - - - - - - - - *

\(\displaystyle \text{The denominator is: }\(\text{W watches}) \:=\:70\%\)


\(\displaystyle \text{Therefore: }\;P(\text{H watches }|\text{ W watches}) \;=\;\frac{40\%}{70\%} \;=\;\frac{4}{7}\)