# probability of overweight OR female question

• Mar 11th 2011, 09:27 PM
tsang
probability of overweight OR female question

In a certain population, containing an equal number of adult males and females, five percent are overweight. Twenty percent of the overweight are female. One person is selected at random from the population. What is the probability that the person is female OR overweight?

Should I try to calculate $P(Female \cup Overweight)$ ? If that's what I should aim for, how do I do it? I'm so confused.
• Mar 12th 2011, 02:35 AM
mr fantastic
Quote:

Originally Posted by tsang

In a certain population, containing an equal number of adult males and females, five percent are overweight. Twenty percent of the overweight are female. One person is selected at random from the population. What is the probability that the person is female OR overweight?

Should I try to calculate $P(Female \cup Overweight)$ ? If that's what I should aim for, how do I do it? I'm so confused.

$\Pr(F \cup O) = \Pr(F) + \Pr(O) - \Pr(F \cap O)$.

From the given data you know that $\Pr(F) = 0.5$ and you know that $\Pr(O | F) = 0.2$. From this you should be able to calculate $\Pr(F \cap O)$ and hence complete the calculation of $\Pr(F \cup O) = \Pr(F) + \Pr(O) - \Pr(F \cap O)$.

If you need more help, please show all your work and say where you get stuck.
• Mar 12th 2011, 11:36 PM
tsang
Quote:

Originally Posted by mr fantastic
$\Pr(F \cup O) = \Pr(F) + \Pr(O) - \Pr(F \cap O)$.

From the given data you know that $\Pr(F) = 0.5$ and you know that $\Pr(O | F) = 0.2$. From this you should be able to calculate $\Pr(F \cap O)$ and hence complete the calculation of $\Pr(F \cup O) = \Pr(F) + \Pr(O) - \Pr(F \cap O)$.

If you need more help, please show all your work and say where you get stuck.

Thanks a lot, I just couldn't work out how to approach before.
I just wonder about one thing please, how do I know it is P(O/F)=0.2, instead of P(F/O)=0.2? From the question wording, it feels like talking about give overweight is condition, then says the females for overweight is 0.2, so should that be P(F/O)=0.2?
Thanks a lot.
• Mar 12th 2011, 11:57 PM
mr fantastic
Quote:

Originally Posted by tsang
Thanks a lot, I just couldn't work out how to approach before.
I just wonder about one thing please, how do I know it is P(O/F)=0.2, instead of P(F/O)=0.2? From the question wording, it feels like talking about give overweight is condition, then says the females for overweight is 0.2, so should that be P(F/O)=0.2?
Thanks a lot.

Quite right. My mistake. In which case you use Pr(F|O) = 0.2 and Pr(O) = 0.05 to get Pr(F and O).