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 find the probability that the first card is a two and the second card is a ten, we can calculate it step by step:

### Step 1: Probability of the first card being a two
There are four twos in a standard deck of 52 cards. So, the probability of drawing a two first is:

\[
P(\text{first card is a two}) = \frac{4}{52} = \frac{1}{13}
\]

### Step 2: Probability of the second card being a ten
After the first card (a two) has been drawn, there are now 51 cards left in the deck. There are still four tens in the deck. So, the probability of drawing a ten next is:

\[
P(\text{second card is a ten}) = \frac{4}{51}
\]

### Step 3: Combined Probability
To find the combined probability of both events happening (first a two, then a ten), we multiply the two probabilities:

\[
P(\text{first a two and then a ten}) = \frac{1}{13} \times \frac{4}{51} = \frac{4}{663}
\]

### Step 4: Converting to Decimal
Now, convert \(\frac{4}{663}\) to a decimal and round it to three decimal places:

\[
\frac{4}{663} \approx 0.006
\]

Thus, the probability that the first card is a two and the second card is a ten is approximately **0.006**.

### Final Answer:
**A. 0.006**

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Do you have any questions or would you like more details?  
Here are some related questions you can explore:

1. What is the probability of drawing two consecutive aces?
2. How does the probability change if the cards are drawn with replacement?
3. What is the probability of drawing a red card followed by a black card without replacement?
4. How does the probability of drawing two specific cards change if you know the deck is shuffled unfairly?
5. What is the probability of drawing two face cards in succession without replacement?
6. How does the calculation differ if the cards are drawn from a partial deck of 30 cards?
7. What is the probability of drawing two cards of the same suit in succession?
8. What is the difference in probability when drawing cards with vs. without replacement?

**Tip:** When solving probability problems, remember to carefully consider whether the events are independent or dependent. This can significantly impact how you calculate the overall probability.

Learn how to calculate the probability of drawing a two and then a ten successively from a standard deck of 52 playing cards. Step-by-step solution provided with clear mathematical formulas and calculations. Suitable for Grades 9-12.

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