the game of scrabble has 100 tiles. the diagram shows the number of tiles for each letter and the letters…

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. find the probability of selecting a letter that precedes t or a letter worth 2 points. the probability of selecting a letter that precedes t or a letter worth 2 points is . (type an integer or a simplified fraction.)

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. find the probability of selecting a letter that precedes t or a letter worth 2 points. the probability of selecting a letter that precedes t or a letter worth 2 points is . (type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Count letters before T

Count the number of tiles for letters A - S. $9 + 2+2 + 4+12+2+3+2+9+4+2+6+8+4+6 = 67$

Step2: Count 2 - point letters

The 2 - point letters are B, C, M, P, V, W, Y. Their total number of tiles is $2 + 2+2+2+2+2+2=14$.

Step3: Find overlapping letters

The overlapping letters (letters before T and worth 2 points) are B, C, M, P, V, W, Y. We've already counted them in both previous steps, so we need to avoid double - counting.

Step4: Calculate probability

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, the total number of tiles is $n = 100$. The number of favorable outcomes is $67 + 14-14=67$. So the probability $P=\frac{67}{100}$.

Answer:

$\frac{67}{100}$