Question

A basket contains 1 blueberry muffin, 1 apple muffin, 1 bran muffin, and 1 carrot muffin. you randomly choose 3 muffins. what is the probability that you choose apple, bran, and carrot muffins? Write in the form of fraction in simplest form.

Answer 1

We have 4 muffins.

The probability of choosing apple first is equal to the number of apple muffins in the basket divided the total number of muffins:

p1 = 1/4

For the second selection we must slect the bran muffin, we do the same as before, but we already selected a muffin, so there are 3 muffins in the basket

p2 = 1/3

For the third selection we have 2 muffins in the basket, so:

p3 = 1/2

the joint probability is:

p = p1*p2*p3 = (1/4)*(1/3)*(1/2) = 1/24

This is if the order matters (first apple, then bran, then carrot)

Now, if we can draw it in any permutation (meaning that the order does not matter), we have 3*2*1 = 6 possible permutations, so the probability is:

P = 6*(1/24) = 1/4

That is equal to the probability of NOT drawing the muffin of blueberry.