Question
You pick a card at random. Without putting the first card back, you pick a second card at random.
1
2
3
4
What is the probability of picking a 4 and then picking a divisor of 36?
Write your answer as a percentage.
%
1
2
3
4
What is the probability of picking a 4 and then picking a divisor of 36?
Write your answer as a percentage.
%
Answers
GPT-4o mini
To find the probability of picking a card with a 4 and then a divisor of 36 from a pack of cards numbered 1 through 4, we first need to determine the total number of cards, the probability of picking a 4, and the probability of picking a divisor of 36 after picking the 4.
1. **Total cards**: There are 4 cards (1, 2, 3, and 4).
2. **Probability of picking a 4 first**:
- There is 1 card with a 4.
- So, the probability of picking a 4 first is \( P(\text{4}) = \frac{1}{4} \).
3. **Divisors of 36**: The divisors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. However, since we only have cards numbered 1 through 4, the relevant divisors of 36 that are also cards in our set are: 1, 2, 3, and 4.
4. **Probability of picking a divisor of 36 after picking a 4**:
- After picking 4, we have 3 cards left (1, 2, and 3).
- All these cards (1, 2, and 3) are divisors of 36.
- So, there are 3 favorable outcomes to pick (1, 2, or 3).
- The probability of picking a divisor of 36 after picking a 4 is \( P(\text{divisor of 36} | \text{4}) = \frac{3}{3} = 1 \).
5. **Total probability**: The total probability of picking a 4 and then picking a divisor of 36 is:
\[
P(\text{4 followed by divisor of 36}) = P(\text{4}) \times P(\text{divisor of 36} | \text{4}) = \frac{1}{4} \times 1 = \frac{1}{4}.
\]
6. **Convert to percentage**:
\[
\frac{1}{4} \times 100\% = 25\%.
\]
Therefore, the final answer is:
\[
\boxed{25\%}.
\]
1. **Total cards**: There are 4 cards (1, 2, 3, and 4).
2. **Probability of picking a 4 first**:
- There is 1 card with a 4.
- So, the probability of picking a 4 first is \( P(\text{4}) = \frac{1}{4} \).
3. **Divisors of 36**: The divisors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. However, since we only have cards numbered 1 through 4, the relevant divisors of 36 that are also cards in our set are: 1, 2, 3, and 4.
4. **Probability of picking a divisor of 36 after picking a 4**:
- After picking 4, we have 3 cards left (1, 2, and 3).
- All these cards (1, 2, and 3) are divisors of 36.
- So, there are 3 favorable outcomes to pick (1, 2, or 3).
- The probability of picking a divisor of 36 after picking a 4 is \( P(\text{divisor of 36} | \text{4}) = \frac{3}{3} = 1 \).
5. **Total probability**: The total probability of picking a 4 and then picking a divisor of 36 is:
\[
P(\text{4 followed by divisor of 36}) = P(\text{4}) \times P(\text{divisor of 36} | \text{4}) = \frac{1}{4} \times 1 = \frac{1}{4}.
\]
6. **Convert to percentage**:
\[
\frac{1}{4} \times 100\% = 25\%.
\]
Therefore, the final answer is:
\[
\boxed{25\%}.
\]