Question

You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 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 an orange hat?

Answer 1

Answer: 1/12

Step-by-step explanation:

The probability of picking a sock as the article of clothing, is 1/4 ... ( 1 out of 4).

The probability of picking color blue is 1/3 ... (1 out of 3)

The probability of picking blue socks, is the product of the 2 individual probabilities.

(1/4) times (1/3) = 1/12

Answer 2

We have a basic problem about probability, we will find that the probability that you randomly end with an orange hat is:

P = 1/12

Now let's see how we got that:

You have:

• 4 pieces of clothing (shirt, pants, socks, or hat)
• 3 colors (purple, blue, or orange)

Only one piece of clothing will change the color. We want to find the probability that you end with an orange hat.

First, we need to find the probability that you randomly select a hat. Assuming all the clothing has the same probability of being selected, the probability will just be one over the number of options (4) then the probability of randomly selecting your hat is: p = 1/4

Now the color is randomly selected, with the same approach as above, the probability of randomly selecting the color orange is: q = 1/3

The joint probability is given by the product of the individual probabilities, then we get:

P = q*p = (1/4)*(1/3) = 1/12

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