To calculate the probability of drawing three hearts consecutively from a 52-card deck without replacement, we follow these steps:

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Step 1: Total number of ways to draw 3 cards

The total number of ways to choose 3 cards from a 52-card deck is given by the combination:

$\binom{52}{3} = \frac{52 \cdot 51 \cdot 50}{3 \cdot 2 \cdot 1} = 22,100$

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Step 2: Number of favorable outcomes

There are 13 hearts in the deck. To draw 3 hearts, the number of favorable outcomes is:

$\binom{13}{3} = \frac{13 \cdot 12 \cdot 11}{3 \cdot 2 \cdot 1} = 286$

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Step 3: Probability of getting 3 hearts

The probability is the ratio of favorable outcomes to total outcomes:

$P(\text{3 hearts}) = \frac{\binom{13}{3}}{\binom{52}{3}} = \frac{286}{22,100} \approx 0.0129$

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Final Answer:

The probability of drawing three hearts is 0.0129, corresponding to Option A.

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Do you want to explore this step-by-step further or ask about related concepts?

Relative Questions:

1. How would the probability change if the cards were replaced each time?
2. What is the probability of drawing 3 spades instead of hearts?
3. How does the probability change if we draw 5 cards instead of 3?
4. What is the general formula for calculating such probabilities?
5. Can this problem be solved using conditional probabilities instead?

Tip:

For problems involving probabilities without replacement, always consider the changing size of the total sample space and favorable outcomes after each draw.