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Machine A produces $60\%$ of the products, which equals $0.60$

Machine B produces $30\%$ of the products, which is $0.30$

The percentage of goods generated by machine C is $10\%=0.10$ while the percentage of items produced by machine A is $10\%=0.10$

The percentage of defective goods generated by machine B is $30\%$, or $0.30$

The percentage of defective goods generated by machine C is $40\%$, or $0.40$

The Bayes theorem $P\left(A\right|B)=\frac{P(A鈭�B)}{P\left(B\right)}$

Let A signify the occurrence of a machine-made object. A. B denotes the occurrence of a machine-made item. The events of a machine-made item are denoted by the letters B. C. Defective items are denoted by the letters C. D. If an item is not faulty, the code ND is used. The following is a tree diagram with the accompanying probabilities:

As stated in the sub part a,

The conditional probabilities are

Using the formula above,

Therefore,

Thus, the required probability is$0.19$

Part b of the subparts

$P\left(D\right)=0.19$

The likelihood that machine A produced the damaged item selected.

The likelihood that machine B produced the damaged item selected.