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A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).
Correct answer is '0.93'. Can you explain this answer?
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A company is hiring to fill four managerial vacancies. The candidates ...
5 men, 3 women
P [atleast one women selected for 4 vacancies]
=1 – P [none]
P [atleast one women selected for 4 vacancies]
=1 – P [none]
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A company is hiring to fill four managerial vacancies. The candidates ...
Probability of selecting at least one woman among four managerial vacancies
Given:
- Five men and three women are candidates for the four managerial vacancies.
- Every candidate is equally likely to be chosen.
To find the probability of at least one woman being selected, we can calculate the probability of the complementary event (no woman being selected) and subtract it from 1.
Finding the probability of no woman being selected:
- Since there are four managerial vacancies, there are four possible outcomes for each vacancy: either a man or a woman can be selected.
- For each vacancy, the probability of selecting a man is 5/8 (since there are five men and eight candidates in total).
- Therefore, the probability of no woman being selected for all four vacancies is (5/8) * (5/8) * (5/8) * (5/8) = (5/8)^4.
Calculating the probability of at least one woman being selected:
- The probability of at least one woman being selected is equal to 1 minus the probability of no woman being selected.
- Therefore, the probability of at least one woman being selected is 1 - (5/8)^4.
Simplifying the calculation:
- (5/8)^4 = (625/4096) ≈ 0.1526 (rounded to 4 decimal places).
- Therefore, the probability of at least one woman being selected is 1 - 0.1526 = 0.8474 (rounded to 4 decimal places).
Rounding off the final answer:
- The final answer should be rounded off to 2 decimal places, which gives us 0.85.
Comparing the answer with the correct answer:
- The correct answer given is 0.93, which is different from the calculated answer of 0.85.
Note:
- It seems that there might be an error in the correct answer provided, as the calculated probability is lower than the given correct answer.
Given:
- Five men and three women are candidates for the four managerial vacancies.
- Every candidate is equally likely to be chosen.
To find the probability of at least one woman being selected, we can calculate the probability of the complementary event (no woman being selected) and subtract it from 1.
Finding the probability of no woman being selected:
- Since there are four managerial vacancies, there are four possible outcomes for each vacancy: either a man or a woman can be selected.
- For each vacancy, the probability of selecting a man is 5/8 (since there are five men and eight candidates in total).
- Therefore, the probability of no woman being selected for all four vacancies is (5/8) * (5/8) * (5/8) * (5/8) = (5/8)^4.
Calculating the probability of at least one woman being selected:
- The probability of at least one woman being selected is equal to 1 minus the probability of no woman being selected.
- Therefore, the probability of at least one woman being selected is 1 - (5/8)^4.
Simplifying the calculation:
- (5/8)^4 = (625/4096) ≈ 0.1526 (rounded to 4 decimal places).
- Therefore, the probability of at least one woman being selected is 1 - 0.1526 = 0.8474 (rounded to 4 decimal places).
Rounding off the final answer:
- The final answer should be rounded off to 2 decimal places, which gives us 0.85.
Comparing the answer with the correct answer:
- The correct answer given is 0.93, which is different from the calculated answer of 0.85.
Note:
- It seems that there might be an error in the correct answer provided, as the calculated probability is lower than the given correct answer.
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A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer?
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A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer?.
A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer?.
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A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer?, a detailed solution for A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer? has been provided alongside types of A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).Correct answer is '0.93'. Can you explain this answer? theory, EduRev gives you an
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