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AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS is
- a)0.19
- b)1.22
- c)0.1
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
AMS employs 8 professors on their staff. Their respective probability ...
here 8 professors are there.
Asking atleast 6 of them continue ,
it has 3 cases.
1 all 8 professors continue.
2 7 professors continue and 1 professors discontinue.
3 6 professors continue and 2 professors discontinue.
1st case all 8 continue is = 2/10*3/10*4/10*5/10*6/10*7/10*/8/10*9/10=9factorial/10power8
=362880/100000000
=>0.00363.
2nd case any 7 professors continue, and 1out of 8 discontinue ,8C1 means 8 ways.
= 2/10*3/10.8/10*1/10, (9/10 prodbability professor discontinue then 1/10)
in this way if we calculate for 8 possibilities then value is =>0.03733.
3rd case any 6 professors continue and 2out of 8 discontinue , 8C2 means 28 ways.
= 2/10*3/10.2/10*1/10( 2 professors discontinue.
if we calculate for 28 possibilites P value is=>0.1436
=0.00363+0.03733+0.1436=0.18456=
0.19
Most Upvoted Answer
AMS employs 8 professors on their staff. Their respective probability ...
Probability Calculation:
To find the probability that at least 6 out of 8 professors will remain employed for 10 years, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = nCk * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes
- n is the total number of trials
- k is the number of successful trials
- p is the probability of success in a single trial
In this case,
- n = 8 (total number of professors)
- k = 6, 7, 8 (number of professors still employed)
- p = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 (probability of remaining employed for each professor)
Calculating the probabilities for each case:
P(X = 6) = 8C6 * 0.2^6 * (1-0.2)^(8-6) = 28 * 0.2^6 * 0.8^2
P(X = 7) = 8C7 * 0.2^7 * (1-0.2)^(8-7) = 8 * 0.2^7 * 0.8^1
P(X = 8) = 8C8 * 0.2^8 * (1-0.2)^(8-8) = 0.2^8
Adding up the probabilities:
P(at least 6 professors still employed) = P(X = 6) + P(X = 7) + P(X = 8)
= 28 * 0.2^6 * 0.8^2 + 8 * 0.2^7 * 0.8^1 + 0.2^8
= 0.0432 + 0.0128 + 0.0016
= 0.0576
Since the probability is given as 0.19 in the options, it seems that there may be an error in either the question or the options provided. The correct answer cannot be determined with the given information.
To find the probability that at least 6 out of 8 professors will remain employed for 10 years, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = nCk * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes
- n is the total number of trials
- k is the number of successful trials
- p is the probability of success in a single trial
In this case,
- n = 8 (total number of professors)
- k = 6, 7, 8 (number of professors still employed)
- p = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 (probability of remaining employed for each professor)
Calculating the probabilities for each case:
P(X = 6) = 8C6 * 0.2^6 * (1-0.2)^(8-6) = 28 * 0.2^6 * 0.8^2
P(X = 7) = 8C7 * 0.2^7 * (1-0.2)^(8-7) = 8 * 0.2^7 * 0.8^1
P(X = 8) = 8C8 * 0.2^8 * (1-0.2)^(8-8) = 0.2^8
Adding up the probabilities:
P(at least 6 professors still employed) = P(X = 6) + P(X = 7) + P(X = 8)
= 28 * 0.2^6 * 0.8^2 + 8 * 0.2^7 * 0.8^1 + 0.2^8
= 0.0432 + 0.0128 + 0.0016
= 0.0576
Since the probability is given as 0.19 in the options, it seems that there may be an error in either the question or the options provided. The correct answer cannot be determined with the given information.
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AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 6 of them still work in AMS isa)0.19b)1.22c)0.1d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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