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the 1,6,15,20,15,6 come in as part of the answer

the 1,6,15,20,15,6 come in as part of the answer

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...
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Hi,

I understand how to obtain n, p, q and x but where does the 1,6,15,20,15,6 come in as part of the answer?

Thank you.

EXAMPLE 3 Constructing a Binomial Distribution In a survey, U.S. adults were asked to identify which social media platform platform Facebook. Construct a binomial probability distribution for the the survey are randomly selected and asked whether they use the social media they use. The results are shown in the figure. Six adults who participated i number of adults who respond yes. (Source: Pew Research) 68% Which Social Media Platforms Do You Use? Facebook and 28% Instagram 26% Pinterest 25% Linkedin 21% Twitter SOLUTION From the figure, you can see that 68% of adults use the social media platform Facebook. So, P = 0.68 and 9 = 0.32. Because n = 6, the possible values of x are 0, 1, 2, 3, 4, 5, and 6. The probabilities of each value of x are P(0) = Co(0.68) °(0.32)6 = 1(0.68) °(0.32) = 0.001 S P(1) = C₁ (0.68) ¹ (0.32) 5 = 6(0.68) ¹ (0.32)³= 0.014 P(2) = 6C₂(0.68) 2 (0.32)4 = 15 (0.68) ² (0.32) 4 0.073 P(3) = 6C3(0.68) ³ (0.32)³ = 20 (0.68) ³ (0.32)³3 = 0.206 P(4) = C4(0.68)*(0.32)² = 15 (0.68) 4 (0.32) ² ≈ 0.328 P(5) = 6C5 (0.68) 5 (0.32)¹ = 6(0.68) 5 (0.32)¹ ≈ 0.279 Rd P(6) = 6C6(0.68)(0.32) = 1(0.68)6(0.32) ≈ 0.099. Notice in the table at the left that all the probabilities are between 0 and 1 that the sum of the probabilities is 1.
Transcribed Image Text:EXAMPLE 3 Constructing a Binomial Distribution In a survey, U.S. adults were asked to identify which social media platform platform Facebook. Construct a binomial probability distribution for the the survey are randomly selected and asked whether they use the social media they use. The results are shown in the figure. Six adults who participated i number of adults who respond yes. (Source: Pew Research) 68% Which Social Media Platforms Do You Use? Facebook and 28% Instagram 26% Pinterest 25% Linkedin 21% Twitter SOLUTION From the figure, you can see that 68% of adults use the social media platform Facebook. So, P = 0.68 and 9 = 0.32. Because n = 6, the possible values of x are 0, 1, 2, 3, 4, 5, and 6. The probabilities of each value of x are P(0) = Co(0.68) °(0.32)6 = 1(0.68) °(0.32) = 0.001 S P(1) = C₁ (0.68) ¹ (0.32) 5 = 6(0.68) ¹ (0.32)³= 0.014 P(2) = 6C₂(0.68) 2 (0.32)4 = 15 (0.68) ² (0.32) 4 0.073 P(3) = 6C3(0.68) ³ (0.32)³ = 20 (0.68) ³ (0.32)³3 = 0.206 P(4) = C4(0.68)*(0.32)² = 15 (0.68) 4 (0.32) ² ≈ 0.328 P(5) = 6C5 (0.68) 5 (0.32)¹ = 6(0.68) 5 (0.32)¹ ≈ 0.279 Rd P(6) = 6C6(0.68)(0.32) = 1(0.68)6(0.32) ≈ 0.099. Notice in the table at the left that all the probabilities are between 0 and 1 that the sum of the probabilities is 1.
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Could you please breakdown probability (P (1)  for me which results in 6, 0.68, squared and results in 0.014 as the final answer.

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