11.10 Binomial Probability Formula 749 TECHNOLOGY TIP Evaluating the Binomial Probability Formula A scientific calculator can be used to evaluate binomial probabilities. In Example 2, the expression C5 2 can first be evaluated using the procedure described in the Technology Tip on page 734. Note that C 10. 5 2 = Then to evaluate the expression 10 , 1 6 2 5 6 3 ( ) ( ) the following key sequence can be entered. 10(1 6) ^2(5 6) ^3ENTER ÷ ÷ To evaluate the binomial probability formula using a TI-84 Plus calculator, we can also use the function binompdf , which stands for binomial probability distribution function . To use this function, we need to enter the following n p x binompdf( , , ), where n p, , and x are from the binomial probability formula. For Example 2, we will enter binompdf(5, 1/6, 2). To do this, we press 2nd VARS , then use the down arrow key to scroll to binompdf( , and then press ENTER. Then type in the following 5 , 1 6 , 2 ) ENTER . ÷ The answer displayed rounds to 0.16075, which matches that obtained in Example 2. The screenshot below shows the calculation on the TI-84 Plus. Example 3 Spring Break According to a survey conducted by OnCampus Research, 20% of college students reported they will work during spring break. Determine the probability that a) exactly 3 of 5 college students randomly selected will work during spring break. b) exactly 4 of 4 college students randomly selected will work during spring break. Solution a) We want to determine the probability that exactly 3 of 5 college students randomly selected will work during spring break. Therefore a college student working during spring break is considered a success. Thus, x 3 = and n 5. = The probability of success, p, is 20%, or 0.2. The probability of failure, q, is 1 0.2, − or 0.8. Substituting these values into the binomial formula yields = = = = = − − P x C p q P C ( ) ( ) (3) ( )(0.2) (0.8) 10(0.2) (0.8) 10(0.008)(0.64) 0.0512 n x x n x 5 3 3 5 3 3 2 Thus, the probability that exactly 3 of 5 randomly selected college students will work during spring break is 0.0512. Comstock/Stockbyte/Getty Images
RkJQdWJsaXNoZXIy NjM5ODQ=