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bionomial distribution

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prashant verma

The document discusses the binomial probability distribution. It defines the binomial distribution as arising from Bernoulli experiments performed n number of times, with exactly two mutually exclusive outcomes of success or failure. It provides the key characteristics of the binomial distribution, such as the experiments consisting of n identical trials where each trial is independent and has the same probability p of success. It also gives the formula for the binomial distribution and provides two examples of calculating probabilities for binomial experiments.

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QUANTTATIVE TECHNIQUES SUBMITTED BY: RITU NEMA PRAJIT MOHANAN PRASHANT VERMA Presentation on BIONOMIAL PROBABLITY DISTRIBUTION
 A random experiment with only two outcomes is a result of Bernoulli's experiment.  One outcome is labeled ‘p’ (success), other is ‘q’ (failure).  P= p(success)+q(failure)  Example: If we consider heads as success, then tails will definitely be a failure.  A binomial distribution arises when Bernoulli’s experiment is performed ‘n’ number of times. Bernoulli Experiment
 The Binomial Distribution is one of the discrete probability distribution.  It is used when there are exactly two mutually exclusive outcomes of a trial.  These outcomes are appropriately labeled Success and Failure.  The Binomial Distribution is used to obtain the probability of observing r successes in n trials, with the probability of success on a single trial denoted by p. BIONOMIAL DISTRIBUTION
 The experiment consists of a sequence of n identical trials.  Each outcome must be classified as a success (p) or a failure (q).  The probability distribution is discrete.  Each trial is independent and therefore the probability of success and the probability of failure is the same for each trial. CHARACTERSTICS
FORMULA
 If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices. Example 1
SOLOUTION  In this case n = 5, X = 3, and p = 1/5, since there is one chance in five of guessing a correct answer. Then,
A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of.. (a) more than 2 hits? (b) at least 3 misses? EXAMPLE 2
SOLUTION
bionomial distribution

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bionomial distribution

  • 1. QUANTTATIVE TECHNIQUES SUBMITTED BY: RITU NEMA PRAJIT MOHANAN PRASHANT VERMA Presentation on BIONOMIAL PROBABLITY DISTRIBUTION
  • 2.  A random experiment with only two outcomes is a result of Bernoulli's experiment.  One outcome is labeled ‘p’ (success), other is ‘q’ (failure).  P= p(success)+q(failure)  Example: If we consider heads as success, then tails will definitely be a failure.  A binomial distribution arises when Bernoulli’s experiment is performed ‘n’ number of times. Bernoulli Experiment
  • 3.  The Binomial Distribution is one of the discrete probability distribution.  It is used when there are exactly two mutually exclusive outcomes of a trial.  These outcomes are appropriately labeled Success and Failure.  The Binomial Distribution is used to obtain the probability of observing r successes in n trials, with the probability of success on a single trial denoted by p. BIONOMIAL DISTRIBUTION
  • 4.  The experiment consists of a sequence of n identical trials.  Each outcome must be classified as a success (p) or a failure (q).  The probability distribution is discrete.  Each trial is independent and therefore the probability of success and the probability of failure is the same for each trial. CHARACTERSTICS
  • 6.  If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices. Example 1
  • 7. SOLOUTION  In this case n = 5, X = 3, and p = 1/5, since there is one chance in five of guessing a correct answer. Then,
  • 8. A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of.. (a) more than 2 hits? (b) at least 3 misses? EXAMPLE 2