Questions: What are the odds against drawing a consonant?

What are the odds against drawing a consonant?
Transcript text: What are the odds against drawing a consonant?
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Solution

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Solution Steps

To find the odds against drawing a consonant, we first need to identify which tiles are consonants and count them. Then, we count the total number of tiles. The odds against drawing a consonant are calculated as the ratio of the number of non-consonant tiles to the number of consonant tiles.

Step 1: Identify Consonant Tiles

First, we identify the consonant tiles from the given set of tiles. The consonants in the set are \( C, D, J, K, \) and \( R \).

Step 2: Count Consonant and Total Tiles

Next, we count the number of consonant tiles and the total number of tiles. The consonant tiles are \( C, D, J, K, R, R \), which gives us a total of 6 consonant tiles. The total number of tiles is 10.

Step 3: Calculate Non-Consonant Tiles

We calculate the number of non-consonant tiles by subtracting the number of consonant tiles from the total number of tiles: \[ \text{Non-consonant tiles} = 10 - 6 = 4 \]

Step 4: Calculate Odds Against Drawing a Consonant

The odds against drawing a consonant are given by the ratio of the number of non-consonant tiles to the number of consonant tiles: \[ \text{Odds against consonant} = \frac{4}{6} = \frac{2}{3} \]

Final Answer

The odds against drawing a consonant are \(\boxed{\frac{2}{3}}\).

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