Engineering
Mathematics
Conditional Probability
Question

The probability that A, B and C can solve a problem are 45,23 and 37  respectively. The probability of the problem being solved by A and B is 815, B and C is 27, A and C is 1235. The probability of the problem being solved by all the three is  835.
Find the probability that the problem can be solved by at least one of them.

101105

98105

97105

103105

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Solution
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P(A) = 4/5

P(B) = 2/3 

P(C) = 3/7

P(ABC)=835

 PAB=815

P(B⋂C) = 2/7

P(A⋂C) = 12/35

 P(at liast ane) = P(AUBUC)

=P(A) + P(B) + P(C)

– P(A⋂B) – P(B⋂C)

+ P(A⋂B⋂C)

=45+23+3781527 1235

+835

=84+70+4556303624105

=101105=107105

=101105.

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