Probability

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an off number of times is:

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 1/2, is :

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(X = 4), then the sum of the mean and the variance of X is:

Five numbers x₁, x₂, x₃, x₄, x₅ are randomly selected from the numbers 1, 2, 3,., 18 and are arranged in the increasing order (x₁ < x < x < x < x). The probability that x = 7 and x = 11 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 :

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3,4,5, otherwise X takes the value -1. Then the expected value of X, is

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

If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + xg(x³) is divisible by x² + x + 1, then P(1) 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 :

Let f:[-3, 1] → R be given as f(x) = { min{(x+6), x²}, if -3 ≤ x ≤ 0; max{√x, x²}, if 0 ≤ x ≤ 1 }. If the area bounded by y=f(x) and x-axis is A, then the value of 6A is equal to ______.