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 a random variable $(x)$ follows binomial distribution with mean 5 and variance 4 , and $5^{23} P(X=3)=\lambda 4^\lambda$, then what is the value of...

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 p...

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 eq...

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 $p + q$?

Three dice are thrown. What is the probability of getting a sum which is a perfect square?

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 ?

Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?

Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?

The probability that a person recovers from a disease is 0.8. What is the probability that exactly 2 persons out of 5 will recover from the disea...

Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty...

A fair coin is tossed 6 times. What is the probability of getting a result in the 6th toss which is different from those obtained in th...

In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly...

What is the probability that all three boys sit together?

What is the probability that boys and girls sit alternatively?

What is the probability that no two girls sit together?

What is the probability that P and Q take the two end positions?

What is the probability that Q and U sit together?

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 ?

A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probability of getting tail in all th...

A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is probability of getting exactly thre...

Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = $\frac{4}{5}$, what is t...

One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the...

Three dice are thrown. What is the probability that each face shows only multiples of 3 ? 

What is the probability that the month of December has 5 Sundays ?

A natural number n is chosen from the first 50 natural numbers. What is the probability that $n+\frac{50}{n}<50 $ ?...