Binomial Probability- Suppose that a trial or an experiment whose outcome can be classified as either success or failure is performed.
Suppose now that n independent rials , each of which results in a success with probability p and in a failure with probability 1-p , are to be performed.
Let X be no of successs that occur in the n trials then X is said to be binomial Random variable with parameter (n,p)
Condition of Binomial distribution\[\frac{n!}{(n-x)!x!}(p^x)(1-p)^{n-x}\]
- Only two outcomes are possible namely success and failure.
- Probability of success p and failure 1-p does not change from trial to trial.
- The trials are statistically independent.
Probability of getteing x success from n trials is given by the bionomial distribution formula.
\[\frac{n!}{(n-r)!x!}(p^x)(1-p)^{n-x}\].
Example -A box contains 10 screws , 3 of which are defective . 2 screws are drawn at random with replacement . The probability that none of the two is defective will be
solution.
here n=2
x=0
p=p(defective)=0.3
Therfore P(x=0)= \[\frac{2!}{(2-0)!0!}(0.3^x)(1-0.3)^{2-0}\]=0.49
