Probability of combined Events

[wadidaw]

A box contains three yelo pens,five red pens and a black pen. Two pens are chosen at random from the box. Calculate the probability that both pens chosen are of the same colour?

 

[Romsek]

look at yellow pens

[MATH]P[\text{choose two yellow pens}] = \dfrac{3}{9}\dfrac{2}{8} = \dfrac{1}{12}[/MATH]
On the first draw there are 3 yellow pens out of 9 pens total.
On the second draw there are 2 yellow pens out of 8 pens total.

Now you do the calculation for red pens.

Add the two for the total probability of drawing two like colored pens.

(Hopefully it's clear you won't draw two black pens)

 

[wadidaw]

look at yellow pens

[MATH]P[\text{choose two yellow pens}] = \dfrac{3}{9}\dfrac{2}{8} = \dfrac{1}{12}[/MATH]
On the first draw there are 3 yellow pens out of 9 pens total.
On the second draw there are 2 yellow pens out of 8 pens total.

Now you do the calculation for red pens.

Add the two for the total probability of drawing two like colored pens.

(Hopefully it's clear you won't draw two black pens)

Thanks