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A Bernoulli trial with success probability p = .2 is repeated independently 15 times. What is the probability that the second, fourth, and tenth of the tries wer successes, but all the other tries were failures? %3D vere

A Bernoulli trial with success probability p = .2 is repeated independently 15 times. What is the probability that the second, fourth, and tenth of the tries wer successes, but all the other tries were failures? %3D vere

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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**Question 19:** A Bernoulli trial with success probability \( p = 0.2 \) is repeated independently 15 times. What is the probability that the second, fourth, and tenth of the tries were successes, but all the other tries were failures? Options: - (A) \( C(15, 3) (0.2)^3 (0.8)^{12} \) - (B) \( (0.2)^3 \) - (C) \( (0.2)^3 (0.8)^{12} \) - (D) \( 1 - C(15, 12) (0.2)^3 (0.8)^{12} \) - (E) \( C(15, 12) (0.2)^3 (0.8)^{12} \) - (F) None of the above --- **Explanation of Answer Choices:** In this problem, we are calculating the probability of having successes specifically on the second, fourth, and tenth tries, with failures on all other tries. - **(A)**: This option uses a combination formula which is not necessary since the specific positions of successful trials are given. - **(B)**: This represents the probability of success for three trials, not considering failures. - **(C)**: This option correctly accounts for the success on three specified trials and failure on the remaining twelve by using the respective probabilities. - **(D)**: This option suggests subtracting the result of a binomial probability from 1, which is incorrect in this context. - **(E)**: This similarly uses a combination for selecting 12 successes from 15 trials, which does not fit the specific positions required. - **(F)**: Indicates that none of the provided options is correct. The correct representation of the experiment, given that positions for successes and failures are fixed, is option (C).
Transcribed Image Text:**Question 19:** A Bernoulli trial with success probability \( p = 0.2 \) is repeated independently 15 times. What is the probability that the second, fourth, and tenth of the tries were successes, but all the other tries were failures? Options: - (A) \( C(15, 3) (0.2)^3 (0.8)^{12} \) - (B) \( (0.2)^3 \) - (C) \( (0.2)^3 (0.8)^{12} \) - (D) \( 1 - C(15, 12) (0.2)^3 (0.8)^{12} \) - (E) \( C(15, 12) (0.2)^3 (0.8)^{12} \) - (F) None of the above --- **Explanation of Answer Choices:** In this problem, we are calculating the probability of having successes specifically on the second, fourth, and tenth tries, with failures on all other tries. - **(A)**: This option uses a combination formula which is not necessary since the specific positions of successful trials are given. - **(B)**: This represents the probability of success for three trials, not considering failures. - **(C)**: This option correctly accounts for the success on three specified trials and failure on the remaining twelve by using the respective probabilities. - **(D)**: This option suggests subtracting the result of a binomial probability from 1, which is incorrect in this context. - **(E)**: This similarly uses a combination for selecting 12 successes from 15 trials, which does not fit the specific positions required. - **(F)**: Indicates that none of the provided options is correct. The correct representation of the experiment, given that positions for successes and failures are fixed, is option (C).
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