In a bag of a few scrabble tiles, there are the letters “T”, “T”, “T”, “O”, “O”, “E”. The probability of drawing two tiles of the same letter one after another without replacement is…
Question
In a bag of a few scrabble tiles, there are the letters “T”, “T”, “T”, “O”, “O”, “E”. The probability of drawing two tiles of the same letter one after another without replacement is…
Solution
To solve this problem, we need to calculate the probability of drawing two tiles of the same letter one after the other without replacement.
Step 1: Identify the total number of tiles We have 3 "T"s, 2 "O"s, and 1 "E". So, the total number of tiles is 3 + 2 + 1 = 6.
Step 2: Calculate the probability of drawing the first tile The probability of drawing any tile is 1, because we are sure to draw a tile.
Step 3: Calculate the probability of drawing a second tile of the same letter If the first tile drawn was a "T", the probability of drawing another "T" is 2/5 (because there are 2 "T"s left and 5 tiles in total). If the first tile drawn was an "O", the probability of drawing another "O" is 1/5 (because there is 1 "O" left and 5 tiles in total). If the first tile drawn was an "E", the probability of drawing another "E" is 0 (because there are no "E"s left).
Step 4: Calculate the total probability The total probability is the sum of the probabilities of drawing two "T"s and two "O"s, because these are the only possibilities to draw two tiles of the same letter. So, the total probability is (1 * 2/5) + (1 * 1/5) = 0.6.
So, the probability of drawing two tiles of the same letter one after another without replacement is 0.6 or 60%.
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