Question

26 cards numbered from 1 to 26. One card is chosen. Probability that it is not divisible by $4$ is
$\left( 1 \right)\text{ }3/13$
$\left( 2 \right)\text{ 4}/13$
$\left( 3 \right)\text{ 2}/13$
$\left( 4 \right)\text{ 10}/13$

Answer 1

In this question we have been given $26$ cards which are numbered from $1$ to $26$. We have to find the probability that a single chosen card is not divisible by $4$. We will solve this question by first finding the total number of cards which are divisible by $4$. We will then subtract that from $26$ to get the number of cards which are not divisible by $4$. We will then find the probability by dividing that number by $26$ to get the required solution.

Complete step-by-step solution:
We know that there are $26$ cards numbered from $1$ to $26$ therefore, all the cards which are divisible by $4$ are:
\Rightarrow \left\\{ 4,8,12,16,20,24 \right\\}
We can see that there are total $6$ cards which are divisible by $4$ out of $26$ cards. Therefore, the number of cards which are not divisible by $4$ will be:
$\Rightarrow 26-6$
On simplifying, we get:
$\Rightarrow 20$
Now the probability that a chosen card is not divisible by $4$, will be:
$\Rightarrow P=\dfrac{20}{26}$
On simplifying the term, we get:
$\Rightarrow P=\dfrac{10}{13}$, which is the required probability.
Therefore, the correct answer is option $\left( 4 \right)$.

Note: It is to be noted that the formula for probability is given by the number of favorable outcomes divided by the number of total outcomes. In the above question we have total outcomes as $26$. Because we have a total of $26$ cards. It is to be noted that probability can never be negative or exceed $1$.