Probability questions
692 published questions with worked solutions.
- Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random...
- If a random variable X follows the Binomial distribution B(33, p) such that 3P(X = 0) = P(X = 1), then the value of P(X=15)...
- A random variable X has the following probability distribution: | x | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | k |...
- If A and B are two events such that P(A) = 1/3, P(B) = 1/5 and P(A B) = 1/2, then P(A|B') + P(B|A') is equal to
- If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of...
- A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is 1/n. If...
- Let E_ 1 and E_ 2 be two events such that the conditional probabilities P(E_ 1 | E_ 2 ) = 1/2, P(E_ 2 | E_ 1 ) = 3/4 and P(E_ 1...
- Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X 2) is equal to
- The mean and variance of a binomial distribution are and /3 respectively. If P(X = 1) = 4/243, then P(X = 4 or 5) is equal to :
- Let E_ 1 , E_ 2 , E_ 3 be three mutually exclusive events such that P(E_ 1 ) = (2 + 3p)/6, P(E_ 2 ) = (2 − p)/8 and P(E_ 3 ) = (1...
- Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then...
- Let S = 1, 2, 3, 4, 5, 6 . Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :
- Two dice are thrown independently. Let A be the event that the number appeared on the 1^ st die is less than the number appeared...
- In a binomial distribution B(n, p), the sum and the product of the mean and the variance are 5 and 6 respectively, then 6(n + p –...
- A signal which can be green or red with probability 4 5 and 1 5 respectively, is received by station A and then transmitted to...
- Let E and F be two independent events. The probability that exactly one of them occurs is 11 25 and the probability of none of...
- A ship is fitted with three engines E_1, E_2 and E_3. The engines function independently of each other with respective...
- Four fair dice D_1, D_2, D_3 and D_4, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The...
- Let X and Y be two events such that P(X ,| ,Y) = 1 2 , P(Y ,| ,X) = 1 3 and P(X Y) = 1 6 . Which of the following is (are)...
- Four persons independently solve a certain problem correctly with probabilities 1 2 , 3 4 , 1 4 , 1 8 . Then the probability that...
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