Probability questions
692 published questions with worked solutions.
- If a random variable x has the probability distribution x: 0, 1, 2, 3, 4, 5, 6, 7 p(x): 0, 2k, k, 3k, 2k^2, 2k, k^2+k, 7k^2 then...
- Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the...
- A bag contains 10 balls out of which k are red and (10-k) are black, where 0 k 10. If three balls are drawn at random without...
- The probability distribution of a random variable X is given below : | X | 4k | 30 7 k | 32 7 k | 34 7 k | 36 7 k | 38 7 k | 40 7...
- Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the...
- If A and B are two events such that P(A B) = 0.1, and P(A|B) and P(B|A) are the roots of the equation 12x^2-7x+1=0, then the...
- One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1,...
- A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a...
- Let A = [a_ ij ] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix....
- Two number k_1 and k_2 are randomly chosen from the set of natural numbers. Then, the probability that the value of i^ k_1 +i^...
- Let S be the set of all the words that can be formed by arranging all the letters of the word 'GARDEN'. From the set S, one word...
- Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I: Red 3, Blue 2, Green 5 Bag II: Red 4,...
- If the probability that the random variable X takes the value x is given by P(X = x) = k(x+1) 3^ -x , x = 0, 1, 2, 3 , where k is...
- In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, the percentage of...
- Two newspapers A and B are published in a city. It is known that 25% of the city population reads A and 20% reads B while 8%...
- A bag contains 6 white and 4 black balls. A die is rolled once and as many balls as the number obtained on the die are drawn from...
- Let A and B be two events such that P( A B ) = 1 6 , P(A B) = 1 4 and P( A ) = 1 4 , where A stands for the complement of the...
- Let two fair six-faced dice A and B be thrown simultaneously. If E_1 is the event that die A shows up four, E_2 is the event that...
- A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of...
- For three events A, B and C, P (Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs)...
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