To find the probability of hanging the blue painting first and then the green painting, we can follow these steps:
- Total paintings: There are 5 paintings: red, yellow, blue, green, and purple.
- Probability of hanging blue first: Since there are 5 paintings, the probability of choosing the blue painting first is \(\frac{1}{5}\).
- Probability of hanging green second: After hanging the blue painting, 4 paintings remain (red, yellow, green, purple). The probability of then choosing the green painting is \(\frac{1}{4}\).
Now, we multiply these two probabilities together to get the total probability of these two events happening in that order:
\[ P(\text{blue first and green second}) = P(\text{blue first}) \times P(\text{green second}) = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20} \]
None of the provided response options explicitly state \(\frac{1}{20}\), but the calculation itself has been followed correctly.
Among the listed responses:
- Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 4 End Fraction (choice 2) is the correct representation of the probability calculation.
Thus, the final answer is:
\(\text{Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 4 End Fraction}\).
1 answer