Questions: (a) Find the odds in favor of drawing a black card. (b) Find the odds against drawing a face card that is a diamond.

Transcript text: (a) Find the odds in favor of drawing a black card. (b) Find the odds against drawing a face card that is a diamond.

Solution

Solution Steps

Step 1: Identify the total number of cards that meet the selection criteria

Number of cards that meet the criteria: 26

Step 2: Calculate the probability

The formula for probability \(P\) is given by \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the given values, we get \(P = \frac{26}{52}\).

Step 3: Express the probability as a fraction and round

After calculation, the probability is 0.5 and rounded to 2 decimal places, it is 0.5.

Final Answer: The probability of drawing a card that meets the criteria is approximately 0.5.

Step 1: Identify the total number of cards that meet the selection criteria

Number of cards that meet the criteria: 9

Step 2: Calculate the probability

The formula for probability \(P\) is given by \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the given values, we get \(P = \frac{9}{52}\).

Step 3: Express the probability as a fraction and round

After calculation, the probability is 0.173 and rounded to 2 decimal places, it is 0.17.

Final Answer: The probability of drawing a card that meets the criteria is approximately 0.17.

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