Suppose that in a claw game at an arcade, there is a collection of toys that have the following characteristics:

2/5 are red;

3/5 are waterproof;

1/2 are cool.

(When we write that 2/5 are red, this means that 3/5 are not red. But the facts above do not provide any

information about the intersection between the different traits.)

Furthermore:

1/5 are both red and waterproof;

1/5 are both red and cool;

3/10 are both waterproof and cool.

(When we write that 1/5 are both red and waterproof, this contains no information about how cool they

are.)

Finally:

1

1/10 are neither red, waterproof, nor cool. (These are pretty lame toys.)

Since working those claws is so hard, suppose that any toy in the game has an equal chance of being selected.

1. (3 points) Draw an area diagram to represent these events. For as many of the events that you can,

compute the probability (for example, P(R \ C \W))).

2. (3 points) What is the probability of drawing a toy that is red and waterproof and cool?

3. (3 points) Suppose that you pull out a toy at random, and you observe only the color, noting that it

is red. Conditional on just this information, what is the probability that the toy is not cool?

4. (3 points) Given that a randomly selected toy is either red or waterproof, what is the probability that

it is cool?