The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will get an electric contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that he will get both?

1 Answer
Ramchandran A.
Nov 3, 2015

#19/45#, The procedure is explained below.

Explanation:

A is the event of getting a plumbing contract and p(A) = #2/3#.
B is the event of getting electrical contract and p(B) = #5/9#.
A#uu#B is the event of getting atleast one of them
p(A#uu#B) = #4/5#.
By addition theorem of probability,
P(A#uu#B) = p(A) + p(B) - p(A#nn#B). where p(A#nn#B) is the probability of getting both the contracts.
P(A#nn#B) = p(A) + p(B) - P(A#uu#B).
i.e. p(A#nn#B) =#2/3# + #5/9# - #4/5# or #(30 + 25 - 36)/45#
p(A#nn#B) = #19/45#

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