Question

a clown made purple and green balloon animals at a party. he kept track of the requests. what is the probability that a randomly selected balloon animal is green and is shaped like a dog? simplify any fractions.

Explanation:

Step1: Find the number of green and dog balloon animals

From the table, the number of green and dog balloon animals is 3.

Step2: Find the total number of balloon animals

Calculate the total: \(3 + 4+ 3+ 3 = 13\)? Wait, no, let's check again. Purple - Giraffe: 3, Green - Giraffe: 4, Purple - Dog: 3, Green - Dog: 3. So total is \(3 + 4+ 3+ 3 = 13\)? Wait, no, 3 (Purple - Giraffe) + 4 (Green - Giraffe) + 3 (Purple - Dog) + 3 (Green - Dog) = 3 + 4 + 3 + 3 = 13? Wait, no, 3 + 4 is 7, 3 + 3 is 6, 7 + 6 is 13? Wait, but the green and dog is 3. Wait, maybe I miscalculated. Wait, Purple - Giraffe: 3, Green - Giraffe: 4, Purple - Dog: 3, Green - Dog: 3. So total number of balloon animals is \(3 + 4+ 3+ 3 = 13\)? Wait, no, 3 (Purple Giraffe) + 4 (Green Giraffe) + 3 (Purple Dog) + 3 (Green Dog) = 3 + 4 = 7, 3 + 3 = 6, 7 + 6 = 13. Then the number of green and dog is 3. So probability is number of favorable outcomes (green and dog) divided by total number of outcomes. So \(P = \frac{3}{3 + 4+ 3+ 3}=\frac{3}{13}\)? Wait, no, wait: Purple - Giraffe: 3, Green - Giraffe: 4, Purple - Dog: 3, Green - Dog: 3. So total is 3 + 4 + 3 + 3 = 13. Favorable is Green - Dog: 3. So probability is \(\frac{3}{13}\)? Wait, but let's check again. Wait, maybe I added wrong. 3 (Purple Giraffe) + 4 (Green Giraffe) = 7 (giraffes), 3 (Purple Dog) + 3 (Green Dog) = 6 (dogs). Total is 7 + 6 = 13. Green and Dog: 3. So yes, probability is \(\frac{3}{13}\). Wait, but maybe I made a mistake in the table. Let me re - examine the table:

The table has columns Purple and Green (for color), and rows Giraffe and Dog (for animal). So:

• Purple - Giraffe: 3
• Green - Giraffe: 4
• Purple - Dog: 3
• Green - Dog: 3

So total number of balloon animals: \(3 + 4+ 3+ 3 = 13\)

Number of green and dog balloon animals: 3

So probability \(P=\frac{\text{Number of green and dog}}{\text{Total number}}=\frac{3}{13}\)

Answer:

\(\frac{3}{13}\)