Please show us what you have tried and exactly where you are stuck.The sample includes 30% of women and 70% of men. It is known that among them 10% of women and 60% of men smoke. Person X is known to be a non-smoker. Find the probability that X is male.
I have calculated non-smokers as fol:- 60% are smokers so 40% are non-smoker males. 40% of 70 men make 28. And 10% of females are smokers. so 90% of 30 females make 27. Total non-smokers becomes 28+27 = 55. Now, to find the probability of X to be a male as well as a non-smoker:-You need to know exactly what the event that you want the probability of before continuing.
You want the probability that .
You will get another hint from me after you answer my question above or show some attempt in solving this problem.
The sample includes 30% of women and 70% of men. It is known that among them 10% of women and 60% of men smoke. Person X is known to be a non-smoker. Find the probability that X is male.
I have calculated non-smokers as fol:- 60% are smokers so 40% are non-smoker males. 40% of 70 men make 28. And 10% of females are smokers. so 90% of 30 females make 27. Total non-smokers becomes 28+27 = 55. Now, to find the probability of X to be a male as well as a non-smoker:-
Probability of non-smoker X = 28/70 ?
or should it be 28/100?
Or even 28/55?
@mrahroy, You realize, I hope, that this answers the wrong question, though it shows all the details of the method for solving the right question:You are given: [math]\text{Pr(Male) = .30 , Pr(Female)=.70,Pr(Smoker|Male) = .60, Pr(Smoker|Female) = .10}[/math]The goal is to find:[math]\text{Pr(Male | Smoker)}[/math]Using conditional probability (aka Bayesian's Probability) we have: [math]\text{Pr(Male | Smoker)} = \frac{\text{Pr(Smoker} \cap \text{Male)}}{\text{Pr(Smoker)}}[/math]First, focus on the numerator. Again, using conditional probability, it can be rewritten as: [math]\text{Pr(Male}\cap \text{Smoker}) = \text{Pr(Smoker | Male)*Pr(Male)}[/math]Next, the denominator. Using the Law of Total Probability & conditional probability: [math]\text{Pr(Smoker)} = \text{Pr(Smoker} \cap \text{Male}) + \text{Pr(Smoker} \cap \text{Female}) = \text{Pr(Smoker|Male)*Pr(Male) + Pr(Smoker|Female)*Pr(Female)}[/math]Putting it all together:
[math]\text{Pr(Male | Smoker)} =\frac{\text{Pr(Smoker | Male)*Pr(Male)}}{\text{Pr(Smoker|Male)*Pr(Male) + Pr(Smoker|Female)*Pr(Female)}}[/math]Hopes this help you understand Bayesian's Probability more concretely.
Your work had the right numerator, and just need to decide on the denominator.The sample includes 30% of women and 70% of men. It is known that among them 10% of women and 60% of men smoke. Person X is known to be a non-smoker. Find the probability that X is male.