# Binomial Essay

501 Words3 Pages
Applications of Binomial Theorem * Help us to expand algebraic expressions easily and conveniently. * Help us with simple numerical estimations * Working with polynomials * Powerful technique for solving probability questions ( used in statistics to calculate the binomial distribution ) * Useful in our economy to find the chances of profit and loss which done great deal with developing economy * Used in forecast services * Architecture * E.g: A man put \$1000 into a bank at an interest rate of 12% per annum, compounded monthly. How much interest can he get in 5 months, correct to nearest dollar? * After 6 months, the amount will be 1000 x (1.01)5 * (1.01)5 = (1 + 0.01)5 = 1 + 5(0.01) + 10(0.01)2 + 10(0.01)3 + 5(0.01)4 + (0.01)5 * Since nearest dollar, so we take only the first 3 terms and ignore the rest. * We have (1.01)5 = 1.051 * Thus amount is approx. \$1051 and the interest is approx. \$51 * E.g: Estimate the value of (1.0309)6 correct to 3 decimal places. * Sources: http://www.mathdb.org/notes_download/elementary/algebra/ae_A3.pdf Binomial Distribution: When you have a binomial distribution, these criteria are met: - There is a set number of trials, n - There are only two possible outcomes from each trial, a success and a failure - The probability of success, p, is fixed - Each trial is independent of the other trials If we have only two outcomes then: p(success) = p p(failure) = 1 - p We want the probability of getting "k" successes. That means we must be successful k times and fail n - k times. So lets say k=3, n=5, and p=0.7, that means: P(success) AND P(success) AND P(success) AND P(failure) AND P(failure) AND keywords in probability mean multipy: P(success) * P(success) * P(success) * [1-P(success)] * [1-P(success)] 0.7 * 0.7 * 0.7 * 0.3 * 0.3 (0.7)^3 * (0.3)^2 So in a