Question

A letter is chosen at random from the letters of the word MATHEMATICIAN. Find the probability that the chosen letter is $M$ or $A$

Answer 1

There are $13$ letters in the word MATHEMATICIAN. $\therefore n\left(S\right)=13$
Let $E$ be the event of getting the letter $M$. $\therefore n\left(E\right)=2$
$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{2}{13}$
Let $F$ be the event of getting the letter $A$. $\therefore n\left(F\right)=3$
$\therefore P\left(F\right)=\frac{n\left(F\right)}{n\left(S\right)}=\frac{3}{13}$
Now, $E$ and $F$ are mutually exclusive events.
$P(E\cup F)=P\left(E\right)+P\left(F\right)=\frac{2}{13}+\frac{3}{13}=\frac{5}{13}$