Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for discoloration, and 27 were found to be discolored. A total of 562 stones were neither cracked nor discolored. One of the 600 stones is selected at random.
a. Find the probability that it is cracked, discolored, or both.
b. Find the probability that it is both cracked and discolored.
c. Find the probability that it is cracked but not discolored.
(a) Since 562 stones were neither cracked nor discolored, 38 stones were cracked, discolored, or both. The probability is therefore 38?600 = 0.0633.
(b) Let A be the event that the stone is cracked and let B be the event that the stone is discolored. We need to find P(A ? B). We know that P(A) = 15?600 = 0.025 and P(B) = 27?600 = 0.045. From part (a) we know that P(A 
B) = 38?600.
Now P(A B) = P(A) + P(B)?P(A ? B). Substituting, we find that 38?600 = 15?600+27?600?P(A ? B). It follows that P(A ? B) = 4?600 = 0.0067.
(c) We need to find 
. Now P(A) = P(A ? B) + (this can be seen from a Venn diagram). We know that P(A) = 15?600 and P(A ? B) = 4?600. Therefore = 11?600 = 0.0183.
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