Binomial Probability Assessment Test Quiz

Explanation
A Binomial probability has two possible outcomes: success or failure. It is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. Therefore, the correct answer is 2.

Explanation
In an experiment where a coin is tossed, there are two possible outcomes: heads or tails. Therefore, the correct answer is 2.

Explanation
The first variable n in a Binomial experiment shows the number of times the experiment is performed. This means that n represents the total number of trials or repetitions in the experiment. It indicates how many times the event or outcome being studied will be observed or tested.

Explanation
In binomial probability experiments, the number of trials must be fixed because the binomial distribution is based on a fixed number of independent trials, each with only two possible outcomes (success or failure). The probability of success and failure remains constant for each trial, and the number of trials determines the shape and characteristics of the binomial distribution. Therefore, it is necessary to have a fixed number of trials in order to accurately calculate and analyze the probabilities in a binomial experiment.

Explanation
In Binomial Distribution, each trial must be independent. This means that the outcome of one trial does not affect the outcome of any other trial. Each trial is considered to be separate and unrelated to the others. This is a fundamental assumption in the binomial distribution, as it allows for the calculation of probabilities based on the number of successes and failures in a fixed number of independent trials.

Explanation
The statement "The probability of success is the same as that of failure" is not always true. In most cases, the probability of success and failure are not equal. The probability of success depends on various factors such as skills, effort, and external circumstances. It is possible for the probability of success to be higher or lower than the probability of failure. Therefore, the correct answer is "Not all time."

Explanation
The probability of getting 2 reds can be calculated by multiplying the probability of getting a red light on the first try (which is 1/3) with the probability of getting another red light on the second try (which is 1/3). Therefore, the probability of getting 2 reds is (1/3) * (1/3) = 1/9 = 0.111. Since none of the given options match this probability, the correct answer is not available.

Explanation
The probability of getting exactly 6 heads when a coin is tossed 10 times can be calculated using the binomial probability formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success in a single trial. In this case, n=10, k=6, and p=0.5 (assuming a fair coin). Plugging these values into the formula, we get P(X=6) = (10 choose 6) * 0.5^6 * (1-0.5)^(10-6) = 210 * 0.5^6 * 0.5^4 = 210 * 0.015625 * 0.0625 = 0.205078125.

Explanation
The notation n! stands for n-factorial. Factorial is a mathematical operation that represents the product of all positive integers from 1 to n. It is denoted by placing an exclamation mark after the number. For example, 5! is equal to 5 x 4 x 3 x 2 x 1, which equals 120.

Explanation
A binomial experiment is one that consists of a fixed number of independent trials, each with two possible outcomes (success or failure), and a constant probability of success. Tossing a coin, asking 200 people if they have a car, and rolling a die to see if a 5 appears all meet these criteria. However, rolling a die until a 6 appears does not have a fixed number of trials, as the number of rolls can vary. Therefore, it is not a binomial experiment.