4 2 B Finding Binomial Probabilities Binomial Probability
4. 2 B – Finding Binomial Probabilities • Binomial Probability Formula n. Cxpᵡqᶮ ᵡ n MATH PRB n. Cr 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) = ₇C₀(. 36)⁰(. 64)⁷≈. 044 = binompdf(7, . 36, 0) P(1) = ₇C₁(. 36)(. 64)⁶≈. 173 = binompdf(7, . 36, 1) P(2) = ₇C₂(. 36)²(. 64)⁵≈. 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = • 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? ₂₅₀C₁₇₈(. 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? ₂₅₀C₁₇₈(. 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? ₂₅₀C₁₇₈(. 71)˄178(. 29)˄72 = binompdf(250, . 71, 178)≈. 056 • 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? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? ₂₅₀C₁₇₈(. 71)˄178(. 29)˄72 = binompdf(250, . 71, 178)≈. 056 • 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? ₁₀C₄(. 75)⁴(. 25)⁶
Examples: • 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? ₂₅₀C₁₇₈(. 71)˄178(. 29)˄72 = binompdf(250, . 71, 178)≈. 056 • 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? ₁₀C₄(. 75)⁴(. 25)⁶ = binompdf(10, . 75, 4)
Examples: • 1. 58% own gas grills. Select 100 households. What is probability exactly 65 will own one? ₁₀₀C₆₅(. 58)⁶⁵(. 42)ᶟ⁵ = binompdf(100, . 58, 65) ≈. 03 • 2. 71% use more than 1 topping on hot dog. Select 250 people. What is probability exactly 178 use more than 1 topping? ₂₅₀C₁₇₈(. 71)˄178(. 29)˄72 = binompdf(250, . 71, 178)≈. 056 • 3. 75% of small businesses have website. If 10 are selected what is probability exactly 4 have a web site? ₁₀C₄(. 75)⁴(. 25)⁶ = 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) = ₄C₂(. 41)²(. 59)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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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
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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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. 121 +. 337 =
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) = ₄C₂(. 41)²(. 59)²≈. 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. 351 +. 163 +. 028 =. 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. 121 +. 337 =. 458
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