Question

a game of scrabble has 100 tiles, as shown to the right. the number of tiles for each letter are shown to the right of each tile. the letter’s point value is printed on the tile. two tiles are drawn in succession from scrabble’s 100 tiles. find the probability of selecting an o or a p on the second draw, given that a b was selected on the first draw. the probability of selecting an o or a p on the second draw, given that a b was selected on the first draw is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of remaining tiles

Since one tile (B) is already drawn, the number of remaining tiles is \(n = 100 - 1=99\).

Step2: Find the number of favorable tiles

The number of O - tiles is \(n_O = 8\) and the number of P - tiles is \(n_P=2\). The number of favorable tiles (O or P) is \(n_{O\cup P}=n_O + n_P=8 + 2=10\).

Step3: Calculate the probability

The probability formula for equally - likely outcomes is \(P=\frac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}\). So \(P=\frac{10}{99}\).

Answer:

\(\frac{10}{99}\)