Question: There are 20 people to be selected for a committee of three, consisting of a president, secretary general and a treasurer. What is the probability that a particular Person $A$ will be selected as president or treasurer?
Could you please verify my answer?
${^{19} P_2\over ^{20} P_3}=0.05$
I'm not sure if there is supposed to be some form of adding two permutations in the answer?
Best Answer
Let $P$ denote the event that person A is chosen for president and let $T$ denote the event that person A is chosen for treasurer.
Then the events $P$ and $T$ are mutually exclusive so that:$$\Pr(P\cup T)=\Pr(P)+\Pr(T)=\frac1{20}+\frac1{20}=0.1$$