6. An industry uses three methods, M1,M2, and M3 to manufacture a part. Of all the parts manufactured, 45% are produced by method M1, 32% by method M2, and the rest 23% by method M3. Further it has been noted that 3% of the parts manufactured by method M1 are defective, while 2% manufactured by method M2 and 1.5% by method M3 are defective. A randomly selected part is found to be defective. Find the probability that the part was manufactured by

(a) method M1,

(b) method M2.