Probability - Hobby

Question

Jake is trying to get dressed. He has 8 shirts; short sleeve, long sleeve, polkadots, striped, plaid, red, blue, and yellow, 4 pairs of pants; Jeans, khakis, gym, sweatpants, and 2 different pairs of socks; knee and ankle.

1. How many different combinations does he have to choose from?
2. What is the probability of him picking jeans, a short sleeve shirt, and ankle socks? Write the probability as a fraction.

Answer 1

This is a so-called "counting problem." The number of possible outfits using 8 shirts, 4 pants, and 2 pairs socks is 8 x 4 x 2 = 64 possibilities. You might have learned a formula for this, but if not, just draw a tree diagram or make a list. It would start like this:

short, jeans, knee

short jeans, ankle

short khaki knee

short khaki ankle

short gym knee

short gym ankle

short sweat knee

short sweat ankle

Using only the short sleeved shirt,we get 8 possibilities. There are also 8 possibilities for each of the other types of shirts, so 64 in all.

A probability is always a fraction (in one form or another). The denominator is the total number of possible outcomes, which we already know is 64. The numerator is the number of those outcomes that we would define as a success, We are given that only one outcome would be a success, so that probability of that one even occurring is 1/64.

Best wishes!