You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places.

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Part 1

A.

0.006

B.

0.994

C.

0.500

D.

0.250

To solve this problem, we need to determine the probability of two specific events happening in sequence when drawing two cards from a standard deck of 52 playing cards.

### Step-by-Step Solution:

1. **Total Number of Possible Outcomes:**
   The total number of ways to draw two cards successively from a deck of 52 cards without replacement is calculated using combinations:
   \[
   \text{Total outcomes} = 52 \times 51
   \]

2. **Favorable Outcomes:**
   - The probability that the first card drawn is a two:
     - There are 4 twos in the deck.
     - Probability of drawing a two first: \(\frac{4}{52} = \frac{1}{13}\)
   - The probability that the second card drawn is a ten given that the first card was a two:
     - After drawing a two, there are 51 cards left.
     - There are still 4 tens in the remaining 51 cards.
     - Probability of drawing a ten second: \(\frac{4}{51}\)

3. **Combined Probability:**
   The combined probability of both events (first card is a two and second card is a ten) occurring is found by multiplying the probabilities of each individual event:
   \[
   P(\text{First is a two and second is a ten}) = \left( \frac{4}{52} \right) \times \left( \frac{4}{51} \right)
   \]

   Calculating the product:
   \[
   P(\text{First is a two and second is a ten}) = \frac{4}{52} \times \frac{4}{51} = \frac{1}{13} \times \frac{4}{51} = \frac{4}{663}
   \]

4. **Decimal Form and Rounding:**
   Converting \(\frac{4}{663}\) to decimal form:
   \[
   \frac{4}{663} \approx 0.00603
   \]
   Rounding to three decimal places:
   \[
   0.00603 \approx 0.006
   \]

### Conclusion:
The probability that the first card is a two and the second card is a ten is approximately \(0.006\), which corresponds to option A.

So, the answer is **A. 0.006**.

Would you like further details or have any questions? 

Here are 8 related questions to expand your understanding:

1. What is the probability of drawing two specific cards in any order from a deck of 52 cards?
2. How does the probability change if we replace the cards after each draw?
3. What is the probability of drawing a two and then another two from the deck?
4. How do combinations differ from permutations in calculating probabilities?
5. Can you calculate the probability of drawing a face card first and an ace second?
6. What is the probability of drawing any two cards of the same rank successively?
7. How does the probability change if the deck has jokers included?
8. What is the probability of drawing two consecutive red cards from the deck?

**Tip:** When calculating probabilities involving sequential events, always consider whether the events are independent (with replacement) or dependent (without replacement). This distinction affects the total number of outcomes and the probability of each event.

Learn how to calculate the probability of drawing a two followed by a ten successively from a standard deck of 52 playing cards. This problem involves combinatorics and probability of independent events. Suitable for Grades 10-12.

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