Question
Scatter Plots & Data Analysis Unit Test 22 of 23 Items Question There are 10 cards in a basket—two of each numbered from 1 to 5. Two cards are randomly selected. The first card is replaced before the second card is selected. What is the probability that a 2 is drawn followed by a 4? Express your answer in lowest terms.(1 point)
Answers
Answered by
GPT-4o mini
To find the probability of drawing a 2 followed by a 4 with replacement, we can follow these steps:
1. **Determine the total number of cards**: There are 10 cards in total (2 cards for each number from 1 to 5).
2. **Find the probability of drawing a 2**: There are 2 cards with the number 2. Therefore, the probability of drawing a 2 on the first selection is:
\[
P(2) = \frac{\text{Number of 2s}}{\text{Total number of cards}} = \frac{2}{10} = \frac{1}{5}
\]
3. **Replace the first card**: Since the first card is replaced, the total number of cards remains the same for the second draw.
4. **Find the probability of drawing a 4**: There are also 2 cards with the number 4. Thus, the probability of drawing a 4 on the second selection is:
\[
P(4) = \frac{\text{Number of 4s}}{\text{Total number of cards}} = \frac{2}{10} = \frac{1}{5}
\]
5. **Calculate the combined probability**: Since the two events (drawing a 2 and drawing a 4) are independent (due to replacement), we multiply the probabilities together:
\[
P(2 \text{ followed by } 4) = P(2) \times P(4) = \left( \frac{1}{5} \right) \times \left( \frac{1}{5} \right) = \frac{1}{25}
\]
The probability that a 2 is drawn followed by a 4 is \(\frac{1}{25}\).
Therefore, the final answer in lowest terms is:
\[
\boxed{\frac{1}{25}}
\]
1. **Determine the total number of cards**: There are 10 cards in total (2 cards for each number from 1 to 5).
2. **Find the probability of drawing a 2**: There are 2 cards with the number 2. Therefore, the probability of drawing a 2 on the first selection is:
\[
P(2) = \frac{\text{Number of 2s}}{\text{Total number of cards}} = \frac{2}{10} = \frac{1}{5}
\]
3. **Replace the first card**: Since the first card is replaced, the total number of cards remains the same for the second draw.
4. **Find the probability of drawing a 4**: There are also 2 cards with the number 4. Thus, the probability of drawing a 4 on the second selection is:
\[
P(4) = \frac{\text{Number of 4s}}{\text{Total number of cards}} = \frac{2}{10} = \frac{1}{5}
\]
5. **Calculate the combined probability**: Since the two events (drawing a 2 and drawing a 4) are independent (due to replacement), we multiply the probabilities together:
\[
P(2 \text{ followed by } 4) = P(2) \times P(4) = \left( \frac{1}{5} \right) \times \left( \frac{1}{5} \right) = \frac{1}{25}
\]
The probability that a 2 is drawn followed by a 4 is \(\frac{1}{25}\).
Therefore, the final answer in lowest terms is:
\[
\boxed{\frac{1}{25}}
\]