Question 1193995
<br>
I'll be picky at first....<br>
Each bolt is produced by a single machine.  So the probability that a defective bolts was "manufactured by machines A, B, and C" is zero.<br>
ANSWER: 0<br>
-------------------------------------------------------------------------<br>
Now on to answering the question that the problem MEANT to ask....<br>
To avoid working with multiplication of percentages in decimal form, I would choose a convenient number for the total number of bolts produced and work with the resulting whole numbers.<br>
So suppose the total production is 10,000 bolts. Then...<br>
Production:
A: 25% of 10,000 = 2500
B: 35% of 10,000 = 3500
C: 40% of 10,000 = 4000<br>
Faulty bolts:
A: 5% of 2500 = 125
B: 4% of 3500 = 140
C: 2% of 4000 = 80<br>
Total defective bolts: 125+140+80 = 345<br>
P(a defective bolt was produced by machine A) = 125/345
P(a defective bolt was produced by machine B) = 140/345
P(a defective bolt was produced by machine C) = 80/345<br>
Simplify the fractions or convert to decimals as desired/required.<br>