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

**Exam Question:**

Two numbers are selected at random(without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and variance of X.

**Answer:**

For IBDP Mathematics, you should know:

Two numbers are selected in **5×4 = 20 **ways.

Let P(X) be the probability of **X as the larger number**.

P(2) = 220 (where the combinations are **(1,2) and (2,1)**)

P(3) = 420 (where the combinations are **(1,3),(3,1),(3,2) and (2,3)**)

P(4) = 620 (where the combinations are **(1,4),(4,1),(4,2),(2,4),(3,4) and (4,3)**)

P(5) = 820 (where the combinations are **(1,5),(5,1),(5,2),(2,5),(3,5),(5,3),(5,4) and (4,5)**)

So,**mean =∑5i=2 X × P(X) = 4****variance =∑5i=2 X**^{2}** × P(X) − (∑5i=2 X ×P(X))**^{2}** = 17 − 16 = 1**.

Work hard for your IBDP Mathematics examination!

End of analysis. Great!