Question

Two balls are chosen randomly from a box containing 8 white, 4 red, and 2 green balls to see if you will win any money. Suppose that you win $2 for each red ball selected, you lose $1 for each blue ball selected, and you get nothing for each green ball selected. What is the probability that you will not lose any money?

Answer 1

* ( given that there is 8 white balls. I think this should be Blue balls. Because you loose $1 if you select Blue ball. But in the bag there is no mention of Blue ball. I thnik this white should be blue )*

Let us consider the events when you will not loose any money.

Event 1: choosing 2 red balls.

If you choose 2 red balls you will win $4.

Total number of balls in bag is 14. We are selecting 2 and there is 4 red ball in bag.

So probability of choosing 2 red is =

Event 2: choosing 1 red 1 blue .

If you choose this you will win $1

Here you can choose one red ball from 4 and one blue from 8 .

So probability of one red and one white is=

Event 3: one red one green.

If you choose this you will win $2

You can choose one red from 4 and one green from 2

Probability of one red and one green =

Event 4: 2 are green

If you choose this you will win nothing and loose nothing

You can choose 2 green from 2 .

Probability of choosing 2 green =

Then probability of not loosing any money is

=P(Event 1)+P(Event 2)+P(Event 3)+P(Event 4)

=

= 0.5165