You pick a card at random. Without putting the first card back, you pick a second card at random.
2
3
4
6
7
8

What is the probability of picking a 3 and then picking an odd number?
Write your answer as a fraction or whole number.

Question

You pick a card at random. Without putting the first card back, you pick a second card at random.
2
3
4
6
7
8

What is the probability of picking a 3 and then picking an odd number?
Write your answer as a fraction or whole number.

UpStudy AI · Accepted Answer

Let $$ A $$ be the event of picking a 3 in the first draw and $$ B $$ be the event of picking an odd number in the second draw.

1. **Probability of $$ A $$:**  
   There is one 3 in the deck of 6 cards. Thus,  
   $$
   P(A) = \frac{1}{6}
   $$

2. **Probability of $$ B $$ given $$ A $$:**  
   After picking the 3, 5 cards remain. The odd numbers originally in the deck are 3 and 7. Since 3 is already picked, only 7 remains as an odd card. Thus,  
   $$
   P(B|A) = \frac{1}{5}
   $$

3. **Combined Probability:**  
   The probability of both events occurring is the product:  
   $$
   P(A \text{ and } B) = P(A) \times P(B|A) = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}
   $$

$$
\boxed{\frac{1}{30}}
$$
The probability of picking a 3 first and then an odd number is $$ \frac{1}{30} $$.

You pick a card at random. Without putting the first card back, you pick a second card at random.
2
3
4
6
7
8

What is the probability of picking a 3 and then picking an odd number?
Write your answer as a fraction or whole number.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Probability Questions

You pick a card at random. Without putting the first card back, you pick a second card at random. 2 3 4 6 7 8 What is the probability of picking a 3 and then picking an odd number? Write your answer as a fraction or whole number.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Probability Questions

You pick a card at random. Without putting the first card back, you pick a second card at random.
2
3
4
6
7
8

What is the probability of picking a 3 and then picking an odd number?
Write your answer as a fraction or whole number.