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.