Probability
Description: This quiz is designed to test your understanding of probability, a branch of mathematics that deals with the likelihood of events occurring. | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: probability random variables conditional probability bayes' theorem |
A fair coin is tossed twice. What is the probability of getting two heads?
A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of randomly selecting a blue ball?
A random variable X has a probability distribution given by P(X = x) = k * x^2, where k is a constant and x = 1, 2, 3. Find the value of k.
Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability of both A and B occurring?
A box contains 10 defective items and 90 non-defective items. If two items are randomly selected without replacement, what is the probability that both items are defective?
A survey found that 60% of people prefer coffee, 30% prefer tea, and 10% prefer both coffee and tea. What is the probability that a randomly selected person prefers coffee or tea?
A continuous random variable X has a probability density function given by f(x) = 2x for 0 ≤ x ≤ 1. Find the probability that X is less than or equal to 0.5.
A random variable X follows a normal distribution with mean μ = 10 and standard deviation σ = 2. What is the probability that X is between 6 and 14?
A company claims that their new product will last for at least 100 hours. A consumer group tests the product and finds that the average lifetime is 95 hours with a standard deviation of 10 hours. Assuming the lifetime follows a normal distribution, what is the probability that a randomly selected product will last for more than 100 hours?
A bag contains 4 red balls, 3 blue balls, and 2 green balls. If two balls are randomly selected without replacement, what is the probability that the first ball is red and the second ball is blue?
A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?
A survey found that 40% of people prefer coffee, 30% prefer tea, and 20% prefer both coffee and tea. What is the probability that a randomly selected person prefers only coffee?
A random variable X has a probability mass function given by P(X = x) = 1/6 for x = 1, 2, 3, 4, 5, 6. Find the expected value of X.
A continuous random variable X has a probability density function given by f(x) = 3x^2 for 0 ≤ x ≤ 1. Find the variance of X.
A company claims that their new product will last for at least 100 hours. A consumer group tests the product and finds that the average lifetime is 95 hours with a standard deviation of 10 hours. Assuming the lifetime follows a normal distribution, what is the probability that a randomly selected product will last for less than 80 hours?