# Probability · Mathematics · NDA

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NDA Mathematics 21 April 2024
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?
NDA Mathematics 21 April 2024
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...
NDA Mathematics 21 April 2024
If the letters of the word 'TIRUPATI' are written down at random, then what is the probability that both Ts are always consecutive?
NDA Mathematics 21 April 2024
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...
NDA Mathematics 21 April 2024
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...
NDA Mathematics 21 April 2024
What is the minimum value of $P(A) + P(B)$?
NDA Mathematics 21 April 2024
What is the maximum value of $P(A) + P(B)$?
NDA Mathematics 21 April 2024
What is the minimum value of $P(B \cap C)$?
NDA Mathematics 21 April 2024
What is the maximum value of $P(B \cap C)$?
NDA Mathematics 21 April 2024
What is the value of $n$?
NDA Mathematics 21 April 2024
What is the value of $p + q$?
NDA Mathematics 3 September 2023
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
NDA Mathematics 3 September 2023
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 ?
NDA Mathematics 3 September 2023
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?
NDA Mathematics 3 September 2023
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
NDA Mathematics 3 September 2023
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...
NDA Mathematics 3 September 2023
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...
NDA Mathematics 3 September 2023
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...
NDA Mathematics 3 September 2023
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...
NDA Mathematics 3 September 2023
What is the probability that all three boys sit together?
NDA Mathematics 3 September 2023
What is the probability that boys and girls sit alternatively?
NDA Mathematics 3 September 2023
What is the probability that no two girls sit together?
NDA Mathematics 3 September 2023
What is the probability that P and Q take the two end positions?
NDA Mathematics 3 September 2023
What is the probability that Q and U sit together?
NDA Mathematics 16 April 2023
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 ?
NDA Mathematics 16 April 2023
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...
NDA Mathematics 16 April 2023
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...
NDA Mathematics 16 April 2023
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...
NDA Mathematics 16 April 2023
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...
NDA Mathematics 16 April 2023
Three dice are thrown. What is the probability that each face shows only multiples of 3 ?
NDA Mathematics 16 April 2023
What is the probability that the month of December has 5 Sundays ?
NDA Mathematics 16 April 2023
A natural number n is chosen from the first 50 natural numbers. What is the probability that $n+\frac{50}{n}<50$ ?...
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