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A problem is given to three persons P, Q, R whose respective

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Darknight123
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A problem is given to three persons P, Q, R whose respective [#permalink] New post  21 Aug 2021, 04:44
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A problem is given to three persons P, Q, R whose respective chances of solving it are 2/7, 4/7, 4/9 respectively. What is the probability that the problem is solved?

A.122/147
B.112/141
C.135/156
D.101/150
E.None of These

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Kinshook
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Re: A problem is given to three persons P, Q, R whose respective [#permalink] New post  21 Aug 2021, 05:07
Given: A problem is given to three persons P, Q, R whose respective chances of solving it are 2/7, 4/7, 4/9 respectively.
Asked: What is the probability that the problem is solved?

The probability that the problem is NOT solved =\( (1-\frac{2}{7})(1-\frac{4}{7})(1-\frac{4}{9}) = \frac{5}{7} * \frac{3}{7} * \frac{5}{9} = \frac{25}{147}\)
The probability that the problem is solved = \(1 - \frac{25}{147} = \frac{122}{147}\)

IMO A
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tbhauer
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Re: A problem is given to three persons P, Q, R whose respective [#permalink] New post  21 Aug 2021, 07:05
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for this problem, it is easier to determine the probability the problem is NOT solved, and subtract from one to solve for the probability that the problem IS solved.
P(not solved) = (1- \(\frac{2}{7}\)) * (1- \(\frac{4}{7}\)) * (1- \(\frac{4}{9}\))
= \(\frac{5}{7}\) * \(\frac{3}{7}\) * \(\frac{5}{9}\)
= \(\frac{75}{441}\)
= \(\frac{25}{147}\)
P(solved) = 1 - \(\frac{25}{147}\)
= \(\frac{122}{147}\)
ANS = A
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Koshmarik
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A problem is given to three persons P, Q, R whose respective [#permalink] New post  18 Mar 2023, 09:07
tbhauer wrote:
for this problem, it is easier to determine the probability the problem is NOT solved, and subtract from one to solve for the probability that the problem IS solved.
P(not solved) = (1- \(\frac{2}{7}\)) * (1- \(\frac{4}{7}\)) * (1- \(\frac{4}{9}\))
= \(\frac{5}{7}\) * \(\frac{3}{7}\) * \(\frac{5}{9}\)
= \(\frac{75}{441}\)
= \(\frac{25}{147}\)
P(solved) = 1 - \(\frac{25}{147}\)
= \(\frac{122}{147}\)
ANS = A



Hi. This is a good take on the problem. But I have a question: Why don't we tackle the problem directly, without determining the probability of NOT solving?
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A problem is given to three persons P, Q, R whose respective [#permalink]
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