# 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.Cumulative binomial distributions are calculated differently than when successes can take on only one value.Let's say a discrete random event was the number of persons shot by firearms last year.

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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?

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Probability distributions give us a visual representation of all possible outcomes of some event and the likelihood of obtaining one outcome relative to the other possible outcomes.

A binomial distribution is a specific probability distribution.(a) First, plug the correct value into each variable: Answer: Given a couple has 5 children, the probability that exactly 3 of them are boys is 0.3125.A binomial distribution is one kind of probability distribution used to model the probability of obtaining one of two outcomes, a certain number of times (k), out of a fixed number of trials (N) of a discrete random event.Try it risk-free You have a probability distribution to create, which one do you use? In this lesson, learn about binomial distributions, get examples and criteria for their use, and learn how to calculate the binomial distribution formula.A probability distribution is a function or rule that assigns probabilities of occurrence to each possible outcome of a random event.Let's rewrite the first situation as this: Given a couple has 5 children, what is the probability that 3 or more will be boys?Possible outcomes: boy or girl Fixed number of repeated independent trials: 5Out of 5 trials, either 3, 4, or 5 are boys = success Probability of success (0.5) probability of failure (0.5) = 1.Being shot is neither a favorable nor a successful outcome for the victim, yet it is the outcome we are counting for this discrete variable.The binomial distribution is used to model the probabilities of occurrences when specific rules are met. How do we prove definitively that the expected value of this distribution is indeed , we can demonstrate that our intuition matches with the fruits of mathematical rigor. Although intuition is a good tool to guide us, it is not enough to form a mathematical argument and to prove that something is true.

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