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 $ ?...

What is the probability of getting a composite number in the list of natural numbers from 1 to 50?

If n > 7, then what is the probability that C(n, 7) is a multiple of 7?

Two numbers x and y are chosen at random from a set of the first 10 natural numbers. What is the probability that (x + y) is divisible by 4 ?

A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x + $\frac{1}{\text{x}}$&nb...

Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?

If P(A) = 0.5, P(B) = 0.7 and P(A ∩ B) = 0.3, then what is the value of P(A' ∩ B') + P(A' ∩ B) + P(A ∩ B') ?

Five coins are tossed once. What is the probability of getting at most four tails ?

Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15 ?

The probability that a person hits a target is 0.5. What is the probability of at least one hit in 4 shots ?

During war, one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3 out of 5 ships would arrive sa...

A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are

The completion of a construction job may be delayed due to strike. The probability of strike is 0.6. The probability that the construction job gets co...

Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?

What is $P (G \cap \overline T)$ equal to?

What is $P(G | \overline T) $ equal to?

What is $P(\overline T | \overline G)$ equal to?

What is the probability that exactly 3 out of 6 workers suffer from a disease?

What is the probability that no one out of 6 workers suffers from a disease?

What is the probability that at least one out of 6 workers suffer from a disease ?