Question

One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be
not an ace

Answer 1

There are $4$ ace cards

Let $B$ be the event that card drawn is ace

So, $n\left(B\right)=4$

Hence,

Probability card drawn is ace $=P\left(B\right)$

$\begin{array}{c}=\frac{numberofacecards}{totalnumberofcards}\\ =\frac{n\left(A\right)}{n\left(S\right)}\\ =\frac{4}{52}\\ =\frac{1}{13}\end{array}$

Probability that card is not an ace

$\begin{array}{c}P\left(B^{\prime }\right)\\ =1-P\left(B\right)\\ =1-\frac{1}{13}\\ =\frac{13-1}{13}\\ =\frac{12}{13}\end{array}$