**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Probability**

**Exam Question:**

In a factory which manufactures bolts, machines A, B and C manufacture 30%, 50% and 20% of the bolts respectively. Of their output 3%, 4% and 1% respectively are defective bolts. A bolt is drawn at random from the product and is found to be defective. Find the probability that this is not manufactured by machine B.

**Answer:**

For GCSE Mathematics, you should know:

Let **A**, **B **and **C** be the bolts **manufactured **by companies **A**, **B **and **C** respectively, and **D **be the **defective bolts** taken.

**P(A) = 3 / 10, P(B) = 1/2, P(C) = 1/5P(D | A) = 3 / 100, P(D | B) = 4 / 100, P(D | C) = 1 / 100**

Now, the probability that a **defective bolt is drawn from machine B** is:

P(B | D) = P(B) x P(D | B) / P(A) x P(D | A) + P(B) x P(D | B) + P(C) x P(D | C)

P(B | D) = 20 / 31

Hence, the probability that the defected bolt is **NOT **manufactured by machine B is **1 - (20 / 31) = 11 / 31.**

Work hard for your GCSE Mathematics examination!

End of analysis. Great!