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
Nov 3, 2015
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#