SOLUTION: An item produced by a company is susceptible to two types of defects namely, A and B. The probability that an item has defect A is 0.167 . The probability that it has defect

Question 1183059: An item produced by a company is susceptible to two types
of defects namely, A and B. The probability that an
item has defect A is 0.167
. The probability that it has defect
B is 0.125
. Calculate the probability that the item has
(i) Both A and B defects
(ii) Only defect A
(iii) Only defect B
(iv) One defect only
(v) At least one defect
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.
An item produced by a company is susceptible to two types of defects namely, A and B.
The probability that an item has defect A is 0.167.
The probability that it has defect B is 0.125.
Calculate the probability that the item has
(i) Both A and B defects
(ii) Only defect A
(iii) Only defect B
(iv) One defect only
(v) At least one defect
~~~~~~~~~~~~~~

            From the context, I will assume that events A and B are independent.

            The problem is silent about it (which is a deficiency of the post),
            but without this assumption, the problem can not be solved/answered.

(i)    Both A and B defects  P(A and B) = P(A)*P(B) = 0.167*0.125 = 0.020875.


(ii)   Only defect A:        P(A_only) = P(A) - P(A and B) = P(A) - P(A)*P(B) = 0.167 - 0.020875 = 0.146125.


(iiI)  Only defect B:        P(B_only) = P(B) - P(A and B) = P(B) - P(A)*P(B) = 0.125 - 0.020875 = 0.104125.
.

(iv)   One defect only:      P(A_only) + P(B_only) = the sum from (ii) and (iii) = 0.146125 + 0.104125 = 0.25025.


(v)    At least one defect:  P(A or B) = P(A) + P(B) - P(A and B) = 0.167 + 0.125 - 0.020875 = 0.271125

Solved.

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