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(b) Among nine randomly selected goblets, what is the probability that at least two are seconds? To find the probability of "at least two," we must rely on the cumulative distribution function (cdf). Recall our binomial cdf is: X - Bin(n, P): B(x; n, p) = P(X S x) = b(y; n, p). Additionally, when finding the binomial y = 0 probability for a range of values, we can use the addition property. Since this function gives the probability that (X S x), and the probability of, "at least two" can be symbolized by P(X 2 2), we must remember that using the complement rule: P(X 2 x) = 1 - P(X < x). ) = 1 - a(x<[ For this experiment, the formula is: P x 2 Using the addition rule, P(X < 2) = P(0) + P %3D [r) Therefore, P(X 2 2) = 1 - + P

(b) Among nine randomly selected goblets, what is the probability that at least two are seconds? To find the probability of "at least two," we must rely on the cumulative distribution function (cdf). Recall our binomial cdf is: X - Bin(n, P): B(x; n, p) = P(X S x) = b(y; n, p). Additionally, when finding the binomial y = 0 probability for a range of values, we can use the addition property. Since this function gives the probability that (X S x), and the probability of, "at least two" can be symbolized by P(X 2 2), we must remember that using the complement rule: P(X 2 x) = 1 - P(X < x). ) = 1 - a(x<[ For this experiment, the formula is: P x 2 Using the addition rule, P(X < 2) = P(0) + P %3D [r) Therefore, P(X 2 2) = 1 - + P

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(b) Among nine randomly selected goblets, what is the probability that at least two are seconds? To find the probability of "at least two," we must rely on the cumulative distribution function (cdf). Recall our binomial cdf is: X - Bin(n, P): B(x; n, p) = P(X S x) = b(y; n, p). Additionally, when finding the binomial y = 0 probability for a range of values, we can use the addition property. Since this function gives the probability that (X S x), and the probability of, "at least two" can be symbolized by P(X 2 2), we must remember that using the complement rule: P(X 2 x) = 1 - P(X < x). ) -1 - A(x<[ For this experiment, the formula is: P x 2 = Using the addition rule, P(X < 2) = P(0) + P %3D - [oro) + ([ Therefore, P(X 2 2) = 1 - (0) + P
Transcribed Image Text:(b) Among nine randomly selected goblets, what is the probability that at least two are seconds? To find the probability of "at least two," we must rely on the cumulative distribution function (cdf). Recall our binomial cdf is: X - Bin(n, P): B(x; n, p) = P(X S x) = b(y; n, p). Additionally, when finding the binomial y = 0 probability for a range of values, we can use the addition property. Since this function gives the probability that (X S x), and the probability of, "at least two" can be symbolized by P(X 2 2), we must remember that using the complement rule: P(X 2 x) = 1 - P(X < x). ) -1 - A(x<[ For this experiment, the formula is: P x 2 = Using the addition rule, P(X < 2) = P(0) + P %3D - [oro) + ([ Therefore, P(X 2 2) = 1 - (0) + P
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