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What is a binomial distribution?
The binomial distribution is one in which you have repeated trials of an experiment in which the outcomes of the experiment are independent, the probability of the outcome is constant.If there are n trials and the probability of "success" in each trail is p, then the probability of exactly r successes is (nCr)*p^r*(1-p)^(n-r) :where nCr = n!/[r!*(n-r)!]and n! = n*(n-1)*...*3*2*1
What happens to the probability as the number of trials increases?
Probability becomes more accurate the more trials there are.
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
What is the ratio of the number of times an event occurs to the total number of trials?
experimental probability
Is binomial distribution is characterized by situations that are analogous to coin tossing?
Yes it is. For a binomial, there must be a fixed number of trials, the probability must remain constant for trials, trials must be independent, and each outcome must be classified into 2 categories.
What formula is used to find the theoretical probability of an event?
Expected successes= Theoretical Probability · Trials P(event) = Number of possible out comes divided by total number of possible
Why do you use binomials?
Binomials are used when the total of n independent trials take place and one wants to find the probability of r successes, when each success has a probability "p" of occurring. There should be independent trails, Probability of success stays the same for all trials, Fixed number of trials and Two different classifications in order to use binomial distribution.
What is a binomial distribution?
The binomial distribution is one in which you have repeated trials of an experiment in which the outcomes of the experiment are independent, the probability of the outcome is constant.If there are n trials and the probability of "success" in each trail is p, then the probability of exactly r successes is (nCr)*p^r*(1-p)^(n-r) :where nCr = n!/[r!*(n-r)!]and n! = n*(n-1)*...*3*2*1
What is called probability that is based on repeated trials of an experiment?
The probability that is based on repeated trials of an experiment is called empirical or experimental probability. It is calculated by dividing the number of favorable outcomes by the total number of trials conducted. As more trials are performed, the empirical probability tends to converge to the theoretical probability.
What happens to theoretical and experimental probability when you increase the number of trials?
When you increase the number of trials of an aleatory experiment, the experimental probability that is based on the number of trials will approach the theoretical probability.
What type of probability is it when you repeat trials?
It is a compound probability.
What happens to the probability as the number of trials increases?
Probability becomes more accurate the more trials there are.
What probability is based on repeated trials of an experiment?
Experimental Probability
How do you solve for probabilities in binomial distributions?
Suppose you have n trials of an experiment in which the probability of "success" in each trial is p. Then the probability of r successes is: nCr*pr*(1-p)n-r for r = 0, 1, ... n. nCr = n!/[r!*(n-r)!]
What is a probability is based on repeated trials of an experiment?
It is empirical (or experimental) probability.
What happens to experimental probability as the number of trials increases?
The probability from experimental outcomes will approach theoretical probability as the number of trials increases. See related question about 43 out of 53 for a theoretical probability of 0.50
What are the features of a binomial distribution?
An experiment with only two outcomes ("success" and "failure"), a constant probability of success, a number of independent trials. Then, if the probability of a success in a trial is p, the probability of r successes in n trials is nCr*pr*(1-p)(n-r) for r = 0, 1, 2, ..., n. In case the super-and sub-scripts do not work, that is n!/[r!*(n-r)!]*p^r*(1-p)^(n-r)
