Binomial Distribution
• Binomial probability distribution gives us insight into many real life phenomena like number of shots to be fired so that the target has a high chance of getting destroyed. Many situations like quality check of items produced by a plant can be handled easily using Binomial probability concepts.
• This concept becomes useful in lot many cases where the situations can be assumed to be closer to Binomial experiment without much error like cases involving choosing of pieces without replacement.
• Bernoulli trial is a trial which has only two outcomes, usually called success and failure and the probability of success and failure does not change trial to trial.
• A binomial experiment is an experiment that can be regarded as a sequence of n Bernoulli trials.
• Binomial probability distribution is a distribution of probability for different numbers of successes in a sequence of n Bernoulli trials. These probabilities are same as the subsequent terms of the binomial expansion of (q+p)n, where p is the probability of success , q is the probability of failure and p+q = 1.
• The probability of getting r successes and (n  r) failures in n trials is:
P(X = r) = nCrprqn–r, where r = 0, 1, 2, 3, 4, 5, …., n.
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Q1
If the probability of getting defective pens is (1/6), then find the mean and standard deviation for the binomial distribution of defective pens in a total of 600.
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Q2
A and B play a tennis match of 5 games. For every win, they get 2 points and 0 for loosing the game. Find the probability of A getting at least 7 points. Both are equally probable to win a game.
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Q3
Find the binomial distribution whose mean is 9 and whose standard deviation is (3/2).
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Q4
A die is thrown 6 times. If ‘getting an odd number’ is a success, then what is the probability of getting 5 successes?
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