without looking at the picture my instinct is D. 3/8

if this is correct I'll try to explain it

First, picture one of these boards with the pegs in it. We've all seen them before, the ball bounces down from peg to peg until it lands in a slot at the bottom. Once you have this pictured, move on to the reasoning.

If each slot had an equal chance of having the ball land in it the odds would be 1/4 to 1/4 to 1/4 to 1/4 for each slot. All of the probabilities must equal up to 1 because the ball must land in one of the slots.

However, my thought process says that there isn't an equal chance of the ball landing in each of the slots. It is much more likely the ball would land in one of the more middle slots. Here's how it works:

For a ball to land in one of the far end slots (1 or 4) it would have to constantly be bouncing to the left of each peg (in the case of 1) or the right of each peg (in the case of 4) to end up on the far side of the slots. Now if it any point it takes a bounce in the opposite direction it's going to end up in one of the middle to slots. The middle slots aren't nearly as picky, as long as the ball doesn't bounce the same direction each time it'll wind up somewhere in the middle.

Now we know that the odds of the ball landing in 1 are the same as it landing in 4, and the odds of it landing in 2 are the same as 3. So we're looking for a number that is greater than 1/4, but when doubled still leaves room for the odds of 1 and 4.

3/8 is the only answer that makes sense

3/8 for 2
3/8 for 3
6/8 it'll land somewhere in the middle, leaving 2/8 it'll land in either of the extreme slots (1 or 4)

none of the other options work!

Now you could spend a lot more time trying to decipher that horrible drawing and come up with a formula, but why bother? using a little logic and imagination you can come to the correct answer in no time at all