Probability · Mathematics · NDA

A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

If the letters of the word 'TIRUPATI' are written down at random, then what is the probability that both Ts are always consecutive?

Let $m = 77^n$. The index $n$ is given a positive integral value at random. What is the probability that the value of $m$ will have $1$ in the units place?

Three different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the numbers is equal to third number?

What is the minimum value of $P(A) + P(B)$?

What is the maximum value of $P(A) + P(B)$?

What is the minimum value of $P(B \cap C)$?

What is the maximum value of $P(B \cap C)$?

What is the value of $n$?

What is the value of $p + q$?

A, B, C and D are mutually exclusive and exhaustive events.

If 2P(A) = 3P(B) = 4P(C) = 5P(D), then what is 77P(A) equal to ?

Let A and B be two independent events such that

P(A̅) = 0.7, P(B̅) = k, P(A ∪ B) = 0.8, what is the value of k ?

If $\rm P(A\cup B)=\dfrac{5}{6}, P(A\cap B)=\dfrac{1}{3}\:and\:P(\bar A)=\dfrac{1}{2}$, then which of the following is/are correct?

1. A and B are independent events.

2. A and B are mutually exclusive events.

Select the correct answer using the code given below.

If A and B are two events such that $\rm P(A)=\dfrac{3}{4} \:and\: P(B)=\dfrac{5}{8}$, then consider the following statements:

1. The minimum value of P(A ∪ B) is $\dfrac{3}{4}.$

2. The maximum value of P(A ∩ B) is $\dfrac{5}{8}.$

Which of the above statements is/are correct?