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 3 points. the odds in favor of selecting a letter worth 3 points are \\(\square:\square\\). (simplify your answers.)

Explanation:

Step1: Find the number of favorable outcomes

From the diagram, 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 \(a=2 + 3=5\).

Step2: Find the number of unfavorable outcomes

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

Step3: Calculate the odds in favor

The odds in favor of an event is given by the ratio \(a:b\). So the odds in favor of selecting a letter worth 3 points is \(5:95\). Simplifying this ratio (dividing both terms by 5), we get \(1:19\).

Answer:

\(1:19\)