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 an m. the odds in favor of selecting an m are \\(\square:\square\\). (simplify your answers.)

Explanation:

Step1: Determine the number of favorable and unfavorable outcomes

From the diagram, the number of \(M\) tiles is \(2\). So the number of favorable outcomes (\(a\)) for selecting an \(M\) is \(2\).
The total number of tiles is \(n = 100\). The number of unfavorable outcomes (\(b\)) is \(n - a=100 - 2=98\).

Step2: Calculate the odds in favor

The formula for odds in favor of an event \(E\) is \(\text{Odds in favor}=\frac{a}{b}\), where \(a\) is the number of favorable outcomes and \(b\) is the number of unfavorable outcomes.
Substituting \(a = 2\) and \(b = 98\), we get \(\frac{2}{98}=\frac{1}{49}\) (by dividing numerator and denominator by \(2\)).

Answer:

\(1:49\)