Question

the game of scrabble has 100 tiles. the diagram shows the number of tiles for each letter and the letter’s point value. one tile is drawn from scrabble’s 100 tiles. if one tile is drawn from the 100 tiles, find the odds in favor and the odds against selecting a letter worth 3 points. the odds in favor of selecting a letter worth 3 points are \\(\square:\square\\). (simplify your answers.)

Explanation:

Step1: Count the number of favorable outcomes

From the diagram, the letters worth 3 points are \(B\) and \(G\). The number of \(B\) tiles is \(2\) and the number of \(G\) tiles is \(3\). So the number of favorable outcomes \(n(F)=2 + 3=5\).

Step2: Count the number of unfavorable outcomes

The total number of tiles \(n(T)=100\). The number of unfavorable outcomes \(n(U)=100 - 5=95\).

Step3: Calculate the odds in favor

The formula for odds in favor is \(\text{Odds in favor}=\frac{n(F)}{n(U)}\). Substituting \(n(F) = 5\) and \(n(U)=95\), we get \(\frac{5}{95}=\frac{1}{19}\).

Answer:

\(1:19\)