Question

You're at a clothing store that dyes your clothes while you wait. You get to pick from

4

44 pieces of clothing (shirt, pants, socks, or hat) and

3

33 colors (purple, blue, or orange).

If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with socks that aren't blue?

Answer 1

i got 1/12 on. my khan one

Explanation:

Answer 2

The probability that you'll end up with socks that aren't blue is
`(1)/(6)`.

Explanation:

The pieces of clothing available:

X = {shirt, pants, socks and hat}

The color options:

Y = {purple, blue and orange}

So, if a person picks a shirt he/she has 3 color options.

Similarly for pants, socks and hat there are 3 color options each.

That makes 12 possible pieces of clothing.

That is, there are 12 total options available.

Now, compute the probability of selecting a socks as follows:

`P(Socks)=(1)/(4)`

Compute the probability of selecting the color blue as follows:

`P(Blue)=(1)/(3)`

Compute the probability of selecting a socks that are not blue as follows:

`P(Socks\cap not\ Blue)=P(Socks)* [1-P(Blue)]`

`=(1)/(4)* [1-(1)/(3)]`

`=(1)/(4)* (2)/(3)`

`=(1)/(6)`

Thus, the probability that you'll end up with socks that aren't blue is
`(1)/(6)`.