Six hundred paving stones were examined for cracks, and 20 were found to be cracked. The same 600 stones were then examined for discoloration, and 29 were found to be discolored. A total of 562 stones were neither cracked nor discolored. One of the 600 stones is selected at random. Find the probability that it is cracked, discolored, or both.

a) probability that is cracked=1/30 (3.33%)

b) probability that is discoloured = 29/600 (4.83%)

c) probability that is cracked and discoloured = 11/600 (1.83%)

Step-by-step explanation:

assuming that each stone is equally likely to be chosen then defining the events C = the stone is cracked, D = the stone is discoloured, N = the stone is neither cracked or discoloured, then

P (C) = number of favourable outcomes/total number of outcomes = 20 stones/600 stones = 1/30 (3.33%)

P (D) = number of favourable outcomes/total number of outcomes = 29 stones/600 stones = 29/600 (4.83%)

the probability that is discoloured and cracked is P (C∩D), where

P (C∪D) = P (C) + P (D) - P (C∩D)

and

P (C∪D) = 1 - P (N)

thus

1 - P (N) = P (C) + P (D) - P (C∩D)

P (C∩D) = P (N) + P (C) + P (D) - 1

replacing values

P (C∩D) = P (N) + P (C) + P (D) = 562/600 + 20/600 + 29/600 - 1 = 611/600 - 1 = 11/600

thus

P (C∩D) = 11/600 (1.83%)