Probability solution You, a woman with a medical background, are one of 198 applicants for an MBA
programme of whom 81 will be selected. You hear, along the grapevine, on good authority that there were 70 women applicants, of whom 38 were selected. Assess your probabilities of being accepted before and after you receive the grapevine information. 
b)  Is it possible for events A and B in a sample space to have the following probabilities? P(A)=0.5          P(B)=0.8          P(A│B)=0.2
c)  You feel ill at night and you stumble into the bathroom, grab one of three bottles in the dark and take a pill. An hour later you feel really ghastly, and you remember that one of the bottles contains poison and the other two aspirin. Your handy medical text says that 80% of people who take poison will show the same symptoms as you are showing, and that 5% of people taking aspirin will have them. What is the probability that you took the poison given that you have got the symptoms?

For (b), if $\Pr(A|B)=0.2$ $\Pr(B)= 0.8$, then $\Pr(A\cap B)=\Pr(A|B)\Pr(B)=0.16$. Show that this is too small by using a familiar formula.
For (c), let $P$ be the event you took the poison, and $S$ be the event you show the symptoms. You want to find $\Pr(P|S)$. This is $\frac{\Pr(P\cap S)}{\Pr(S)}$.
To find $\Pr(S)$, perhaps draw a suitable tree, noting that $S$ can happen in two ways: (i) You took poison and show symptoms or (ii) You took aspirin and show symptoms.
The probabilities of (i) and (ii) are straightforward to calculate. For example, the probability of (i) is $\left(\frac{1}{3}\right)( 0.80)$.
There remains some calculation to do, but this should provide a good start.
