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29 Apr 2018, 09:22
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C
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71% (00:55) correct
29%
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Harper interviewed for a job with company A and with company B. What is the probability that Harper will get job offers from both companies?
(1) The probability that Harper will get a job offer from exactly one of the companies is 0.6.
(2) The probability that Harper will get a job offer from neither company is 0.1.
(1) The probability that Harper will get a job offer from exactly one of the companies is 0.6.
(2) The probability that Harper will get a job offer from neither company is 0.1.
29 Apr 2018, 12:12
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Solution
Given:
• Harper interviewed for a job with company A and company B
To find:
• The probability that Harper will get job offers from both companies
Approach and Working:
The possible cases are:
• Harper does not get job in any of the companies Or,
• Harper gets jobs in exactly one company Or,
• Harper get job in both the companies
- o Thus, P(o)+P(1)+P(2)=1, Where
- P(0)= Probability that Harper does not get job in any of the company.
- P(1)= Probability that Harper gets jobs in exactly one company
- P(2)= Probability that Harper get job in both the companies
Analysing Statement 1
• As per the information given in Statement 1, probability that Harper will get a job offer from exactly one of the companies = 0.6
- o But this statement does not provide any information about the probability of receiving job offers from none of the companies
- o Thus, statement 1 is not sufficient
Analysing Statement 2
• As per the information given in Statement 2, the probability that Harper will get a job offer from neither company is 0.1
- o But, this statement does not provide any information about the probability of receiving job offers from exactly one of the companies
- o Thus, statement 2 is not sufficient
Combining Both Statements
• We know the probability of receiving offer from exactly one company = 0.6 and probability of receiving offer from none = 0.1
• Therefore, the probability of receiving offer from both the companies = 1 – (0.6 + 0.1) = 0.3
Hence, by combining the statements we get the answer.
Answer: C
29 Apr 2018, 23:58
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Bunuel
Harper interviewed for a job with company A and with company B. What is the probability that Harper will get job offers from both companies?
(1) The probability that Harper will get a job offer from exactly one of the companies is 0.6.
(2) The probability that Harper will get a job offer from neither company is 0.1.
(1) The probability that Harper will get a job offer from exactly one of the companies is 0.6.
(2) The probability that Harper will get a job offer from neither company is 0.1.
Probability to get job offer from \(A\) is \(x\) (not to get is \(1-x\)).
Probability to get job offer from \(B\) is \(y\) (not to get is \(1-y\)).
(1) \(x(1-y)+y(1-x)=0.6\). Clearly, NS.
(2) \((1-x)(1-y)=0.1\). NS, as well.
Combining two statements, we have a system of equations with \(2\) unknowns (\(x\) and \(y\)) and \(2\) equations. We can solve for \(x\) and \(y\), and find \(xy\) (probability to get job offer from both companies). Hence, sufficient.
Answer: C
