Question

a game of scrabble has 100 tiles, as shown to the right. the number of tiles for each letter are shown to the right of each tile. the letters point value is printed on the tile. two tiles are drawn in succession from scrabbles 100 tiles. find the probability of selecting a tile worth 10 points on the first draw and a tile worth 4 points on the second draw. the probability of selecting a tile worth 10 points on the first draw and a tile worth 4 points on the second draw is (type an integer or a simplified fraction)

Explanation:

Step1: Find the number of 10 - point tiles and 4 - point tiles

From the Scrabble tile distribution:

• The 10 - point tiles are \(Q\) (1 tile) and \(Z\) (1 tile), so there are \(n(10)=2\) tiles worth 10 points.
• The 4 - point tiles are \(F\) (2 tiles), \(H\) (2 tiles), \(V\) (2 tiles), \(W\) (2 tiles), \(Y\) (2 tiles), so there are \(n(4)=2 + 2+2+2+2 = 10\) tiles worth 4 points.

Step2: Calculate the probability of the first draw

The probability of drawing a 10 - point tile on the first draw, using the formula \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The total number of tiles is \(N = 100\). So \(P(\text{10 - point first})=\frac{2}{100}\).

Step3: Calculate the probability of the second draw

After drawing one tile (a 10 - point tile) on the first draw, the number of remaining tiles is \(N'=99\).
The probability of drawing a 4 - point tile on the second draw is \(P(\text{4 - point second})=\frac{10}{99}\).

Step4: Use the multiplication rule for dependent events

The multiplication rule for two dependent events \(A\) and \(B\) is \(P(A\cap B)=P(A)\times P(B|A)\).
Here, \(A\) is the event of drawing a 10 - point tile first and \(B\) is the event of drawing a 4 - point tile second.
\(P=\frac{2}{100}\times\frac{10}{99}\)

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Answer:

\(\frac{1}{495}\)