Binomial trials and binomial distribution:

Consider a random experiment the outcomes of which can be classified as success or failure. It means that the experiment results in 2 outcomes only E₁(success) or E₂­ (failure). Assume that experiment can be repeated many times, probability of success or failure in any trial are p and q (p + q = 1) and do not vary from trial to trial and finally different trials are independent. This type of experiment is called as Binomial experiment and trials are said to be binomial trials. For example tossing of a fair coin many times, each time outcome would be either a success or failure.

A probability distribution representing the binomial trials is said to binomial distribution.

Let us consider a Binomial experiment which is repeated 'n' times. Let probability of success and failure in any trial be p and q respectively and we are interested in probability of occurrence of 'r' successes in these n trials. Now number of ways of choosing 'r' success in 'n' trials = ⁿC_r. The probability of 'r' successes and (n-r) failures is p^r×q^n-r. Therefore probability of having exactly r successes =  ⁿC_r×p^r×q^n-r

Let 'X' be random variable representing number of successes, then

                        P(X = r) = ⁿC_r×p^r×q^n-r   (r = 0, 1, 2, L , n)

1 = (p + q)ⁿ = ⁿC₀p⁰qⁿ + ⁿC₁p¹q^{n -1} + ⁿC₂p²q^{n -2} + ....... + ⁿC_rp^rq^{n -r} + ....... + ⁿC_npⁿ X -> Number of success0, 1, 2,......., r,........... n

Remarks:

• The probability of utmost 'r' successes in n trials = 
• The probability of atleast 'r' successes in n trials = 
• The probability of having 1^st success at r^th trial = p×q^r-1

Example:   A die is thrown 7 times. What is chance that the odd  number turns up (i) exactly 4 times (ii) at least 4 times.

Sol:                   The probability of success = 

                                    (i) For the exactly 4 successes required probability = 

                                    (ii) For atleast 4 successes the required probability

Email based Binomial trials and binomial distribution Assignment Help - Homework Help

We at www.expertsmind.com offer email based Binomial trials and binomial distribution assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.

Expertsmind's best education services

• Quality assignment-homework help assistance 24x7 hrs
• Best qualified tutor's network
• Time on delivery
• Quality assurance before delivery
• 100% originality and fresh work