probability

Let M be a randomly chosen non-empty subset of S = {1,2,3,...,2026}. Which of the following is the probability that the product of all the elements of M is even?

Suppose that a computer program provides a non-negative and integer-valued random solution to the equation n₁ + n₂ + n₃ + n₄ = 20. Which of the following is the probability that al...

Let X be an exponentially distributed random variable with mean λ(> 0). If P(X > 5) = 0.35, then the conditional probability P(X > 10|X > 5) is __________. (Rounded off to two deci...

Let L = lim_{n→∞} Σ_{k=0}^{n} (e^{-n} n^k / k!) Which of the following is the value of L?

A clinic specializes in testing for a disease D. The result of the test can be either positive or negative. A study revealed that if a person suffers from the disease D, the test r...

Let X be a random variable that follows Uniform(-1,1) distribution. The conditional distribution of the random variable Y given X = x is the Uniform($x^2 - 0.1, x^2 + 0.1$) distrib...

Let A$_{5 \times 5}$ be a matrix such that each of its elements follows Bernoulli(p = 0.50) distribution independently. The probability that the row-sum of the second row and the c...