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

**Exam Question:**

From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.

**Answer:**

For I/GCSE Mathematics, you should know:

Let X be the **number of defective bulbs drawn** __(out of 4)__ i.e., 0, 1, 2, 3, 4

P(**defective** bulb) = 5/15 = 1/3

Therefore P(**non**-defective bulb) = 1 - 1/3 = 2/3

*P(X = 0) =*^{4}* C*_{0}* x (2/3)*^{4}* = 16/81**P(X = 1) =*^{4}* C*_{1}* x (1/3) x (2/3)*^{3}* = 32/81*

Similarly, finding the probability for X = 2, 3, 4:

Therefore, the mean is **∑xP(x) = 108/81 = 4/3**.

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!