A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is :

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :

Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :

Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be {1 \over 2} and probability of occurrence of 0 at the odd place be {1 \over 3}. Then the probability that '10' is followed by '01' is equal to :

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x2 + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\in$$R, is :

Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $$-$$ k), the probability that exactly one of B and C occurs is (1 $$-$$ 2k), the probability that exactly one of C and A occurs is (1 $$-$$ k) and the probability of all A, B and C occur simultaneously is k2, where 0 < k < 1. Then the probability that at least one of A, B and C occur is :

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $$\times$$ 2 matrices. The probability that such formed matrix have all different entries and are non-singular, is :

Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is k{\left( {{3 \over 4}} \right)^9} then k lies in the set :

A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. the smallest value of n, so that the probability of guessing at least 'n' correct answers is less than {1 \over 2}, is :

Let X be a random variable such that the probability function of a distribution is given by P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty ). Then the mean of the distribution and P(X is positive and even) respectively are :

The probability that a randomly selected 2-digit number belongs to the set {n $$\in$$ N : (2n $$-$$ 2) is a multiple of 3} is equal to :

Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = {5 \over 9}, is :

A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x $$\ge$$ 5 | x > 2) is :

Two fair dice are thrown. The numbers on them are taken as $$\lambda$$ and $$\mu$$, and a system of linear equations x + y + z = 5 x + 2y + 3z = $$\mu$$ x + 3y + $$\lambda$$z = 1 is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

When a certain biased die is rolled, a particular face occurs with probability {1 \over 6} - x and its opposite face occurs with probability {1 \over 6} + x. All other faces occur with probability {1 \over 6}. Note that opposite faces sum to 7 in any die. If 0 < x < {1 \over 6}, and the probability of obtaining total sum = 7, when such a die is rolled twice, is $$13\frac{9}{6}$$, then the value of x is :

Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :

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 :