4.2B – Finding B inomial Probabilities

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4.2B – Finding B inomial Probabilities. Binomial Probability Formula nCxp ᵡ qᶮ ᵡ 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 ). - PowerPoint PPT Presentation

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4.2B Finding Binomial Probabilities

4.2B Finding Binomial ProbabilitiesBinomial Probability FormulanCxpq n MATH PRB nCr x (p)x (q)(n-x)n=# trials, x=#successes, p=probability of success in 1 trialq= probability of failure in 1 trialCalculator2nd VARS 0:binompdf(n,p,x)Probability DistributionList 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 0 1 2 3 4 5 6 7 p(x) .044 .173 .292 .274 .154 .052 .010 .001 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) .032. 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) .032. 71% 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) .032. 71% 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) .032. 71% 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).0563. 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) .032. 71% 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).0563. 75% 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) .032. 71% 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).0563. 75% 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) .032. 71% 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).0563. 75% 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

Examples41% 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.Examples41% 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.Examples41% 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).3512) at least 2 respond yes

3) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)

3) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = 3) Fewer than 2 respond yes.Examples41% 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).3512) 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.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.1633) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = 3) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) =3) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) = .0283) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) = .028 .351 + .163 + .028 =3) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) = .028 .351 + .163 + .028 = .5423) Fewer than 2 respond yes.Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) = .028 .351 + .163 + .028 = .5423) Fewer than 2 respond yes. = P(0) + P(1)P(0)=binompdf(4,.41,0) = Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) = .028 .351 + .163 + .028 = .5423) Fewer than 2 respond yes. = P(0) + P(1)P(0)=binompdf(4,.41,0) = .121Examples41% 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).3512) at least 2 respond yes = P(2) + P(3) + P(4)P(2)=.351 P(3) = binompdf(4,.41,3) =.163P(4) = binompdf(4,.41,4) = .028 .351 + .163 + .028 = .5423) Fewer than 2 respond yes. = P(0) + P(1)P(0)=binompdf(4,.41,0) = .121 P(1) = binompdf(4,.