Question

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 564 stones were neither cracked nor discolored. One of these 600 stones is chosen at random. What is the probability that it is both cracked and distorted?

Answer 1

Answer: 0.01

Step-by-step explanation:

Let the events are :

C = paving stones found to be cracked.

D = paving stones found to be discolored.

Given : Total stones : T = 600  (i)

C = 15

D=  27

C'∩D'=  564   (ii)

Since C'∩D' = (C∪D)' = T- C∪D         (iii)

From (i) , (ii)and (ii) , we have

564 = 600- C∪D

⇒ C∪D=600- 564= 36

Formula : C∩D= C+D- C∪D

Put values , we get

C∩D= 15+27-36=6

Now ,

$P(C\cap D)=\dfrac{C\cap D}{T}=\dfrac{6}{600}=0.01$

The probability that it is both cracked and distorted is 0.01.