Probability Exercise with Answer | Example 3

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.

2. Calculate the probability of drawing two balls of the same color.

We call event B: “Two balls of the same color are drawn.”

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

We have:  P(B)= P(A)+P(N)

So:

So:    

                              

b) Calculate:

                         

* 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.

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