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The board game Scrabble® contains 100 tiles, 98 of which are labeled with a letter and a point value, and 2 blank tiles. The distribution of tiles and point values is shown in the table. A tile is drawn at random. Find the probability of each event. (Enter your probabilities as fractions.)

a. Drawing a tile that is worth 1 point

 

b. Drawing a tile that is worth 10 points

 

d. Drawing a tile that is worth at least 4 points

 Apr 4, 2023
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To find the probability of each event, we need to know the number of tiles with the desired point value and divide it by the total number of tiles. The distribution of tiles and point values is missing in your message, but I can provide the standard distribution used in the game:

Point value | Tiles

1 point | E ×12, A ×9, I ×9, O ×8, N ×6, R ×6, T ×6, L ×4, S ×4, U ×4

2 points | D ×4, G ×3

3 points | B ×2, C ×2, M ×2, P ×2

4 points | F ×2, H ×2, V ×2, W ×2, Y ×2

5 points | K ×1

8 points | J ×1, X ×1

10 points | Q ×1, Z ×1

a. Drawing a tile that is worth 1 point:

There are 12 + 9 + 9 + 8 + 6 + 6 + 6 + 4 + 4 + 4 = 68 tiles worth 1 point.

The probability of drawing a 1-point tile is 68/100 = 17/25.

b. Drawing a tile that is worth 10 points:

There are 1 + 1 = 2 tiles worth 10 points (Q and Z).

The probability of drawing a 10-point tile is 2/100 = 1/50.

d. Drawing a tile that is worth at least 4 points:

To find the probability of drawing a tile worth at least 4 points, we can count the number of tiles worth 4 points or more. There are 2 + 2 + 2 + 2 + 2 + 1 + 1 + 1 + 1 = 14 tiles worth 4 points or more (F, H, V, W, Y, K, J, X, Q, Z). The probability of drawing a tile worth at least 4 points is 14/100 = 7/50.

 Apr 4, 2023

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