# 4.2B â€“ Finding Binomial Probabilities Binomial Probability Formula...

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### Transcript of 4.2B â€“ Finding Binomial Probabilities Binomial Probability Formula...

4.2B Finding Binomial Probabilities Binomial Probability Formula nCxpq n MATH PRB nCr x (p)x (q)(n-x) n=# trials, x=#successes, p=probability of success in 1 trial q= probability of failure in 1 trial Calculator 2 nd VARS 0:binompdf(n,p,x) Probability Distribution List of possible values of x with each corresponding probability in a table. Example: 7 participants (#trials) 36% answered yes (p=.36) (q=.64) Binomial probability distribution for # responding yes. P(0) = C(.36)(.64).044 = binompdf(7,.36,0) P(1) = C(.36)(.64).173 = binompdf(7,.36,1) P(2) = C(.36)(.64).292 = binompdf(7,.36,2) etc. x p(x) Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? C(.71)178(.29)72 = 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? C(.71)178(.29)72 = binompdf(250,.71,178) 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? C(.71)178(.29)72 = binompdf(250,.71,178) % of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? C(.71)178(.29)72 = binompdf(250,.71,178) % of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? C(.75)(.25) Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? C(.71)178(.29)72 = binompdf(250,.71,178) % of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? C(.75)(.25) = binompdf(10,.75,4) Examples: 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? C(.58)(.42) = binompdf(100,.58,65) % use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? C(.71)178(.29)72 = binompdf(250,.71,178) % of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? C(.75)(.25) = binompdf(10,.75,4) .016 Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) 2) at least 2 respond yes 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59) 2) at least 2 respond yes 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) = 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) =.028 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = = 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = =.542 3) Fewer than 2 respond yes. Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = =.542 3) Fewer than 2 respond yes. = P(0) + P(1) P(0)=binompdf(4,.41,0) = Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = =.542 3) Fewer than 2 respond yes. = P(0) + P(1) P(0)=binompdf(4,.41,0) =.121 Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = =.542 3) Fewer than 2 respond yes. = P(0) + P(1) P(0)=binompdf(4,.41,0) =.121 P(1) = binompdf(4,.41,1) Examples 41% of women choose reading as favorite leisure activity. 4 are selected What is the probability that they answer yes it is their favorite? 1) exactly 2 respond yes. P(2) = binompdf(4,.41,2) = C(.41)(.59).351 2) at least 2 respond yes = P(2) + P(3) + P(4) P(2)=.351 P(3) = binompdf(4,.41,3) =.163 P(4) = binompdf(4,.41,4) = =.542 3) Fewer than 2 respond yes. = P(0) + P(1) P(0)=binompdf(4,.41,0) =.121 P(1) = binompdf(4,.41,1) =.337

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