Question

At the beginning of a board game, players take turns
drawing 7 lettered tiles. Are drawing A's on the first two tiles dependent or
independent events? Explain.

Answer 1

The second pick is dependent on the first one.

Let $a$ be the number of tiles with the letter A, and $n$ be the total number of tiles.

With the first pick, you have probability $\frac{a}{n}$ to pick an A, because you have $a$ "good" cases out of $n$ possible cases.

The second pick depends on the first one:

• If you pick an A tile on the first pick, the probability of picking another A is now $\frac{a-1}{n-1}$

• If you didn't pick an A tile on the first pick, the probability of picking another A is now $\frac{a}{n-1}$