Hello, simone!

1. The figure shown represents a board with four rows of pegs,

and at the bottom of the board are four cells numbered 1 to 4.

When the ball shown passes between two adjacent pegs in the same row,

it will hit the peg directly beneath the opening.

The ball then has probability ½ of passing to the left or right of that peg.

What is the probability that when the ball will end up in cell 2? Code:

o
↓
* ↓ *
↓
* a *
½/ \½
* b c *
½/ \½ /½
* d e * *
½\ /½
|_______|___o___|_______|_______|
1 2 3 4

There are three paths for the ball to finish in cell 2:

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This can also be solved with the Binomial Expansion.