Problem 14E

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.

Solution :

Step 1 of 3

Given the total stones is 600.

Then 600 stones are selected randomly.

562 is the total stones were neither cracked nor discolored.

a).

Now we have to find the probability that it is cracked,discolored,or both.

Let A is the total stones is 600 and

Let B is the total stones were neither cracked nor discolored is 562

P(cracked,discolored,or both) = P(A)-P(B)

P(cracked,discolored,or both) = 600-562

P(cracked,discolored,or both) = 38

Therefore the probability that it is cracked,discolored,or both is 38.