## Probability Exercise

A bowl contains n black balls (n ∈ N *) and two oval balls.

We draw two balls in a row from this bowl without repeating before the next drawing.

**1.** What is the probability of drawing two white balls?

**2.** We denote by Un the probability of drawing two balls of the same color.

**a)** Express Un in terms of n.

**b) **Calculate:

### * Interpret the result.

**The solution**

**1. Calculate the probability of drawing two white balls.**

We call event A: “drawing two white balls.”and from it:

P(A) is the number of appropriate cases for the event A division The number of possible cases for this experiment.

We call the event N: “drawing two black balls.”

We have: P(B)= P(A)+P(N)

So:

*** Interpretation of the result.**

This result is interpreted as when the number of black balls is large enough, then event N becomes a sure event. In other words, in this case, there is no effect for two white balls.