In a group,40%of the items are red. Of all the red items in the group,30%also have stripes. What percentage of the items in the group are red with stripes?

1. Break Down the Problem

To find the percentage of items that are red with stripes, follow these steps:

• Determine the percentage of the total items that are red.
• Find the percentage of red items that have stripes.
• Calculate the percentage of the total items that are red with stripes by combining the two percentages.

2. Relevant Concepts

• Percentage of red items: $P_{\text{red}} = 40\%$
• Percentage of red items that have stripes: $P_{\text{stripes} | \text{red}} = 30\%$

3. Analysis and Detail

Using the formula for the percentage of red items that also have stripes: $P_{\text{red with stripes}} = P_{\text{red}} \times P_{\text{stripes} | \text{red}}$ Substituting the given values: $P_{\text{red with stripes}} = 40\% \times 30\%$

Calculating step-by-step: $P_{\text{red with stripes}} = 0.40 \times 0.30 = 0.12$ Converting to percentage: $P_{\text{red with stripes}} = 0.12 \times 100\% = 12\%$

4. Verify and Summarize

The calculation indicates that 12% of the total items in the group are red with stripes. This result is consistent with the percentages provided in the problem statement.

Final Answer

12% of the items in the group are red with stripes.