Question

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

Answer 1

Step 1: Use the formula of probability:

$P\left(A\right)=\frac{\text{number of outcome favorable to A}}{\text{total number of Possible outcome}}$

or

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

where,

1. $P\left(A\right)$ is probability of an event ‘$A$’
2. $n\left(A\right)$ is the favorable outcome of the event ‘$A$’
3. $n\left(S\right)$ is total number of possible outcomes in a sample space

Step 2: Find the total number of possible outcomes

ln a pack of 52 cards it has four suites that are hearts, clubs, spades, diamonds.

Each suite has thirteen cards that are ace, $2,3,4,5,6,7,8,9,10$ jack, queen and king.

$S$ is a sample space of all the possible outcomes which is $52$

Thus, total number of possible outcomes in a sample space is,

$n\left(S\right)=52$

Step 3: Find the probability of getting an ace:

Out of $52$ outcomes only $4$ contain chances of getting an ace

Thus, the favorable outcome of the event is,

$n\left(A\right)=4$

$\text{Required probability=}\frac{4}{52}=\frac{1}{13}$

Step 4: Find the probability of getting a face card

Out of $52$ outcomes only $12$ contain a chance of getting a face card (king, queen, jack)

Thus, the favorable outcome of the event is,

$n\left(A\right)=12$

$\text{Required probability=}\frac{12}{52}=\frac{3}{13}$

Step 6: Find the probability of getting Any card number from $2$ to $10$

Any card number from $2$ to $10$ are in total of four sets.

So, the possibility of getting any card from $2$ to $10$ is $36$ out of $52$

Thus, the favorable outcome of the event is,

$n\left(A\right)=36$

$\text{Required probability=}\frac{36}{52}=\frac{9}{13}$

Hence, the probability of an ace is $\frac{1}{13}$,a face card is $\frac{3}{13}$, any card numbered from $2$ to $10$ is $\frac{9}{13}$