NDA Mathematics Probability Medium Questions

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 ?

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 ?

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 ?

Let A, B, C and D be mutually exclusive and exhaustive events and $\frac{P(A)}{2}=\frac{P(B)}{3}=\frac{P(C)}{5}=\frac{P(D)}{8}$. What is $P(A)+P(B)+P(C)$ equal to ?

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 ?

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

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

Four dice are rolled. What is the probability that the total of the numbers on the dice is 6 ?

Consider the following statements in respect of the events $A,B,C$ :

I. $(A\cup B\cup C)\cap (\overline{A}\cap \overline{B}\cap \overline{C})$ is an impossible event.

II. $(A\cap B\cap C)\cap (\overline{A}\cup \overline{B}\cup \overline{C})$ is a possible event.

Which of the statements given above is/are correct ?

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?

Four dice are rolled.
What is the probability that getting a total of the numbers on the dice is at least $23$ ?

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

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

In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is $90\%$. If he gets the correct answer to a question, then what is the probability that he was guessing ?