Question

the game of scrabble has 100 tiles. the diagram shows the number of tiles for each letter and the letters point - value. one tile is drawn from scrabbles 100 tiles. if one tile is drawn from the 100 tiles, find the odds in favor and the odds against selecting a letter worth 8 points.

Explanation:

Step1: Count favorable outcomes

From the given tile - point values, the letters worth 8 points are X (1 tile) and Z (1 tile), so the number of favorable outcomes $n(F)=2$.

Step2: Count non - favorable outcomes

The total number of tiles is $n(T) = 100$. The number of non - favorable outcomes $n(N)=100 - 2=98$.

Step3: Calculate odds in favor

The odds in favor of an event is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. So, odds in favor $=\frac{n(F)}{n(N)}=\frac{2}{98}=\frac{1}{49}$.

Step4: Calculate odds against

The odds against an event is the ratio of the number of non - favorable outcomes to the number of favorable outcomes. So, odds against $=\frac{n(N)}{n(F)}=\frac{98}{2}=49$.

Answer:

The odds in favor of selecting a letter worth 8 points is $1:49$ and the odds against selecting a letter worth 8 points is $49:1$.