# Thread: Probibality problem, Pls help

1. ## Probibality problem, Pls help

A market research study is being conducted to determine if a product modification will be well received by the public. A total of 910 consumers are questioned regarding this product. The table below provides information regarding this sample.

_______Positive Reaction.....Neutral Reaction.....Negative Reaction
Male............190....................70......... .................110
Female..........210...................200......... ................130

(a) What is the probability that a randomly selected male would find this change unfavorable (negative)?
(b) What is the probability that a randomly selected person would be a female who had a positive reaction?
(c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

2. Originally Posted by stoorrey
(a) What is the probability that a randomly selected male would find this change unfavorable (negative)?
= number on males with negative reaction divided by the total number of males

Originally Posted by stoorrey
(b) What is the probability that a randomly selected person would be a female who had a positive reaction?
= number of females with a positive reaction divided by the total number of people

Originally Posted by stoorrey
(c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

This is conditional probabilty, let A be the person with a negative reaction and B be a male

You require $P(B/A) = \frac{P(A\cap B)}{P(A)}$

3. ## Thanks a lot

Thanks a lot for your help pickslides

but pls can you elaborate part c a bit more

i dont know how to use the formula.

4. $P(B/A) = \frac{P(A\cap B)}{P(A)}$

= (number of males with a negative reaction divided by total number of people in the survey) divided by (number of people (males + females) with a negative reaction divided by total number of people in the survey)

5. Originally Posted by pickslides
$P(B/A) = \frac{P(A\cap B)}{P(A)}$

= (number of males with a negative reaction divided by total number of people in the survey) divided by (number of people (males + females) with a negative reaction divided by total number of people in the survey)
Doesn't a condition alter the sample space? So shouldn't the answer be:

(number of males with a negative reaction)/(total number of people with a negative reaction)

The math works out the same way as in your solution, however your logic intrigues me.

6. You are correct to say the arithmetic will give the same solution. My explanation is from the definition in the equation supplied. Yours is a simplification knowing the number of total people surveyed will cancel out.

7. Hello, stoorrey!

pickslides is absolutely correct.
Vitruvian's approach to part (c) is also correct and more direct.

A market research study is being conducted to determine if a product modification
will be well received by the public.
A total of 980 consumers are questioned regarding this product.
The table below provides information regarding this sample.

$\begin{array}{c||c|c|c||c|}
& \text{Positive} & \text{Neutral} & \text{Negative} & \text{Total} \\ \hline \hline
\text{Male} & 190 & 70 & 110 & 370 \\ \hline
\text{Female} & 210 & 200 & 130 & 610 \\ \hline\hline\
\text{Total} & 400 & 340 & 240 & 980 \\ \hline \end{array}$
(a) What is the probability that a randomly selected male would have a negative reaction?
$P(\text{neg}\,|\,\text{male}) \;=\;\frac{n(\text{neg} \wedge \text{male})}{n(\text{male})} \;=\;\frac{110}{370} \;=\;\frac{11}{37}$

(b) What is the probability that a randomly selected person would be a female who had a positive reaction?
$P(\text{female}\wedge\text{pos}) \;=\;\frac{n(\text{female}\wedge\text{pos})} {n(\text{Total})} \;=\;\frac{210}{980} \;=\;\frac{3}{14}$

(c) If it is known that a person had a negative reaction to the study,
what is the probability that the person is male?
$P(\text{male}\,|\,\text{neg}) \;=\;\frac{n(\text{neg}\wedge\text{male})} {n(\text{neg})} \;=\;\frac{110}{240} \;=\;\frac{11}{24}$