Question

A card is drawn from a pack of $52$ playing cards. What is the probability that it is any card numbered from $2$ to $10$?

Answer 1

Step 1 Finding the favorable outcomes:

There are $52$ cards in a deck which are in $4$ suits.

In each suit, there are $9$ cards numbered from $2$ to $10$.

So, there are $4\times 9=36$ cards in all that are numbered from $2$ to $10$.

So, the favourable outcomes are $36$ and the total outcomes are $52$.

Step 2 Finding probability:

The formula for probability is

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

$$\begin{gathered} \Rightarrow P(cardnumberedfrom2to10)=\frac{36}{52} \\ \therefore P(cardnumberedfrom2to10)=\frac{9}{13} \end{gathered}$$

Hence, the probability of drawing a card numbered from $2$ to $10$ from a pack of $52$ cards is $\frac{9}{13}$.