Question

Bathsheba has 5 paintings in her house, 1 each in a color palette of red, yellow, blue, green, and purple. She hangs them randomly in a horizontal order. What is the probability of hanging the blue painting first, and then the green?(1 point)
Responses

15⋅15
Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 5 End Fraction

15⋅14
Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 4 End Fraction

15
Start Fraction 1 over 5 End Fraction

15+15
Start Fraction 1 over 5 End Fraction plus Start Fraction 1 over 5 End Fraction

Answer 1

To find the probability of hanging the blue painting first and then the green painting, we can follow these steps:

1. **Total paintings**: There are 5 paintings: red, yellow, blue, green, and purple.
2. **Probability of hanging blue first**: Since there are 5 paintings, the probability of choosing the blue painting first is \(\frac{1}{5}\).
3. **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:

\(\text{Start Fraction 1 over 5 End Fraction times Start Fraction 1 over 4 End Fraction}\).