A box contains 10 cards numbered 1 to 10 .
What is the probability of drawing number 3 ?
What is the probability of drawing number 7 and number 8 cards ?

Question

A box contains 10 cards numbered 1 to 10 . What is the probability of drawing number 3 ? What is the probability of drawing number 7 and number 8 cards ?

UpStudy AI · Accepted Answer

**Step 1. Drawing the number 3 card**

- There are $$10$$ cards and only one card is numbered $$3$$.
- Thus, the probability of drawing the number $$3$$ card is  
  $$
  P(3) = \frac{1}{10}.
  $$

**Step 2. Drawing the number 7 and number 8 cards**

Assuming you are drawing two cards without replacement and the order does not matter:

1. The total number of ways to choose $$2$$ cards from $$10$$ is given by the combination  
   $$
   \binom{10}{2} = \frac{10 \times 9}{2} = 45.
   $$
2. There is only one favorable outcome, which is selecting the cards numbered $$7$$ and $$8$$.

Thus, the probability of drawing the cards $$7$$ and $$8$$ together is  
$$
P(7 \text{ and } 8) = \frac{1}{45}.
$$

If you were drawing sequentially, you could also determine the probability as follows:

- The probability of drawing a $$7$$ first is $$\frac{1}{10}$$, then the probability of drawing an $$8$$ is $$\frac{1}{9}$$. This gives  
  $$
  \frac{1}{10} \times \frac{1}{9} = \frac{1}{90}.
  $$
- Similarly, if you draw an $$8$$ first and a $$7$$ second, the probability is also $$\frac{1}{90}$$.
- Since there are two orders, the total probability is  
  $$
  2 \times \frac{1}{90} = \frac{2}{90} = \frac{1}{45}.
  $$

**Final Answers:**

- The probability of drawing the number $$3$$ card is $$\frac{1}{10}$$.
- The probability of drawing the cards numbered $$7$$ and $$8$$ is $$\frac{1}{45}$$.
The probability of drawing the number 3 card is 1/10. The probability of drawing the cards numbered 7 and 8 is 1/45.

A box contains 10 cards numbered 1 to 10 .
What is the probability of drawing number 3 ?
What is the probability of drawing number 7 and number 8 cards ?

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