The first letter of each month is written on a card and the cards are placed in a bag. What isthe probability of pulling out a J, placing it back in the bag, and then drawing an M?

Answer 1

So, to start with, the probability of drawing a J is 3/12 since there is January, July, and June. So there's a 25% chance of getting J first.

There are 2 months starting with M, March and May, so by itself there is a 2/12 chance of that happening, or a roughly 17% chance.

However, since we only care about drawing an M after drawing a J, we have a 3/12 chance of the first draw, and the other 9/12 possibilities we don't care about because they've already failed. So out of the 3/12 times where we draw a J, we then have a 2/12 chance of drawing an M.

So 3/12 * 2/12 = 6/144, about a 4% chance of drawing these letters in this order.

Specifically, 0.04166666