# Binomial Distribution Solved Problems When the successful outcome takes on more than one exact value, then we are looking for the probability of a cumulative binomial distribution.

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To use a binomial distribution, the situation being modeled must adhere to four criteria: When the successful outcome can take on more than one exact value, then we are looking for the probability of a cumulative binomial distribution.

To calculate a binomial distribution, identify the number of independent trials, number of successful trials, and the probability of success, and then evaluate the binomial probability formula. We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities.

Possible outcomes: right or wrong Fixed number of repeated independent trials: 5Out of 5 trials, exactly 2 questions answered correctly = success Probability of success (0.5) probability of failure (0.5) = 1 Given 10 rolls of a die, what is the probability that you will roll the number 1 exactly five times?

Possible outcomes: roll a 1 or roll something other than 1 (i.e., 2, 3, 4, 5, or 6)Fixed number of repeated independent trials: 10Out of 10 trials, exactly five of the rolls land on 1 = success Probability of success (1/6 = 0.17) probability of failure (5/6 = 0.83) = 1 What about when the successful outcome is not exactly one outcome?

Binomial distributions would be used to model situations where the successful outcome is exactly one value. Given a couple has 5 children, what is the probability that exactly 3 will be boys?

Possible outcomes: boy or girl Fixed number of repeated independent trials: 5Out of 5 trials, exactly 3 children are boys = success Probability of success (0.5) probability of failure (0.5) = 1 Given 5 questions on a test, what is the probability of randomly guessing exactly 2 questions correctly?

The binomial distribution formula applies to situations that do not include cumulative probabilities.

To calculate a binomial distribution, you will need to (a) plug the correct value into each variable, (b) find the binomial coefficient, and (c) evaluate the binomial probability formula. Question: Given a couple has 5 children, what is the probability that exactly 3 are boys?

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