Problema Solution
in a wood pile of 39 pieces, 12 are rotten, 23 are to short to use, and 5 are both rotten and to short. What is the probability that a piece is either rotten or too short?
Answer provided by our tutors
Let
event A: the piece is rotten
P(A) = 12/39
event B: the piece is too short
P(B) = 23/39
event A and B: the piece is rotten and too short
P(A and B) = 5/39
event A or B: the piece is either rotten or too short
P(A or B) = P(A) + P(B) - P(A and B), where P(A and B) denotes the probability that A and B both occur at the same time
P(A or B) = 12/39 + 23/39 - 5/39
P(A or B) = (12 +23 - 5)/39
P(A or B) = 30/39
P(A or B) = 0.7692
the probability that a piece is either rotten or too short 0.7692.