Probability — NDA Mathematics PYQs

*Directions : For the next five (05) items that follow :

A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).*

What is the probability that the number selected is divisible by 2 ?

*Directions : For the next five (05) items that follow :

A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).*

What is the probability that the number selected is divisible by 3 ?

*Directions : For the next five (05) items that follow :

A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).*

What is the probability that the number selected is divisible by 4 ?

*Directions : For the next five (05) items that follow :

A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).*

What is the probability that the number selected is divisible by 6 ?

*Directions : For the next five (05) items that follow :

A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).*

What is the probability that the number selected does not contain zero at any position ?

*Directions : For the next three (03) items that follow :

Let $A,B,C$ and $D$ be mutually exclusive and exhaustive events and $\frac{\text{P}(A)}{2}=\frac{\text{P}(B)}{3}=\frac{\text{P}(C)}{5}=\frac{\text{P}(D)}{8}$.*

What is $\text{P}(A)+\text{P}(B)+\text{P}(C)$ equal to ?

*Directions : For the next three (03) items that follow :

Let $A,B,C$ and $D$ be mutually exclusive and exhaustive events and $\frac{\text{P}(A)}{2}=\frac{\text{P}(B)}{3}=\frac{\text{P}(C)}{5}=\frac{\text{P}(D)}{8}$.*

What is $\frac{[2\text{P}(A)+3\text{P}(B)]}{[4\text{P}(C)+5\text{P}(D)]}$ equal to ?

*Directions : For the next three (03) items that follow :

Let $A,B,C$ and $D$ be mutually exclusive and exhaustive events and $\frac{\text{P}(A)}{2}=\frac{\text{P}(B)}{3}=\frac{\text{P}(C)}{5}=\frac{\text{P}(D)}{8}$.*

If $G$ is the geometric mean of $\text{P}(A)$, $\text{P}(B)$, $\text{P}(C)$ and $\text{P}(D)$, then what is $9G$ equal to ?

*Directions : For the next two (02) items that follow :

Four dice are rolled.*

What is the probability that getting a total of the numbers on the dice is 6 ?

*Directions : For the next two (02) items that follow :

Four dice are rolled.*

What is the probability that getting a total of the numbers on the dice is at least 23 ?