Question

A card is drawn from a pack of $52$ cards at random. The probability of getting
Neither an ace nor a king card is:
${\text{A}}{\text{.}}$$\frac{2}{{13}}$
${\text{B}}{\text{.}}$$\frac{{11}}{{13}}$
${\text{C}}{\text{.}}$$\frac{4}{{13}}$
${\text{D}}{\text{.}}$ $\frac{8}{{13}}$

Answer 1

Hint: - Total number of ace cards in a pack of $52$ cards is $4$ and the total Number of king card is $4$. That means the number of required cards in pack is $44$.
We have to find a probability of getting neither an ace nor a king.
As we know:
A deck of cards contains $52$ cards. They are divided into four suits: Spades, diamonds, clubs and hearts each suit has $13$ cards: in which $1$ ace cards and three picture cards: jack, king and queen. In this question we neither need king nor is ace that means number of required cards $44$.
$p\left( A \right) = \frac{{N\left( E \right)}}{{N\left( S \right)}}$
This is the formula of finding the probability of any event $A$ where $N\left( E \right)$is the number of favorable outcomes and $N\left( S \right)$ is total outcomes or sample space.
Probability of getting neither an ace nor a king is=$\frac{{44}}{{52}} = \frac{{11}}{{13}}$
Option ${\text{B}}$ is correct.
Note:-You have to find total number of outcomes and total number of Favorable outcomes and just put in the formulae of finding the Probability. in this type of cards question you should have knowledge of cards distribution.