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 24?

Write your answer as a decimal.

Answer 1

To determine the probability of picking a 4 and then picking a divisor of 24, we first need to identify what the possible cards are and the relevant divisors of 24.

### Step 1: Identify the total cards
Assuming the numbers on the cards are 1, 2, 3, and 4, there are 4 total cards.

### Step 2: Identify the divisors of 24
The divisors of 24 are:
- 1
- 2
- 3
- 4
- 6
- 8
- 12
- 24

From these, only the numbers 1, 2, 3, and 4 are available on the cards. Therefore, the divisors of 24 that we can pick are 1, 2, 3, and 4.

### Step 3: Calculate the probability
#### Probability of picking a 4 first:
Since there are 4 cards total and only one of them is a 4, the probability of picking a 4 first is:
\[
P(\text{pick 4}) = \frac{1}{4}
\]

#### Probability of picking a divisor of 24 second:
After picking a 4, there are 3 cards left (1, 2, and 3) out of which all are divisors of 24. Thus, the probability of picking a divisor of 24 (1, 2, or 3) second is:
\[
P(\text{pick divisor of 24} | \text{picked 4 first}) = \frac{3}{3} = 1
\]

### Step 4: Combined probability
The combined probability of both events occurring (picking a 4 first and then picking a divisor of 24) is calculated by multiplying the individual probabilities:
\[
P(\text{pick 4 and then a divisor of 24}) = P(\text{pick 4}) \times P(\text{pick divisor of 24} | \text{picked 4 first}) = \frac{1}{4} \times 1 = \frac{1}{4}
\]

### Step 5: Convert to decimal
To express the probability as a decimal:
\[
\frac{1}{4} = 0.25
\]

### Final Answer
Thus, the probability of picking a 4 and then picking a divisor of 24 is:
\[
\boxed{0.25}
\]