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 Start Fraction 1 over 5 End Fraction 15+15 Start Fraction 1 over 5 End Fraction plus Start Fraction 1 over 5 End Fraction 15⋅14

Answer 1

To find the probability of hanging the blue painting first and then the green painting second, we can analyze the situation step by step.

1. **Probability of hanging the blue painting first**: There are 5 paintings and only 1 of them is blue. Thus, the probability of picking the blue painting first is:

\[
P(\text{blue first}) = \frac{1}{5}
\]

2. **Probability of hanging the green painting second given that the blue is first**: After hanging the blue painting, there are 4 paintings left, and only 1 of them is green. The probability of picking the green painting second is:

\[
P(\text{green second | blue first}) = \frac{1}{4}
\]

3. **Final probability of both events happening**: To find the combined probability of both events (hanging blue first and green second), we multiply the individual probabilities:

\[
P(\text{blue first and green second}) = P(\text{blue first}) \times P(\text{green second | blue first}) = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20}
\]

Thus, the probability of hanging the blue painting first and then the green painting second is:

\[
\boxed{\frac{1}{20}}
\]