To find the probability of first letting out a white cat followed by a black cat, we can calculate it step by step:
1. Total number of cats: There are 7 white cats and 8 black cats, so the total number of cats in the cage is 7 + 8 = 15.
2. Probability of letting out a white cat first: Since there are 7 white cats out of 15 total cats, the probability of letting out a white cat first is 7/15.
3. Remaining cats: After one white cat has been let out, there are now 6 white cats and 8 black cats left in the cage.
4. Probability of letting out a black cat second: With 8 black cats out of the remaining 14 cats, the probability of letting out a black cat second is 8/14.
5. Calculate the overall probability: To find the probability of both events happening in succession, we multiply the individual probabilities together:
[tex]\( \text{Probability of white cat first} \times \text{Probability of black cat second} \)[/tex]
[tex]\( = \frac{7}{15} \times \frac{8}{14} \)[/tex]
[tex]\( = \frac{56}{210} \)[/tex]
[tex]\( = \frac{4}{15} \)[/tex]
Therefore, the probability of letting out a white cat followed by a black cat is 4/15 or approximately 0.27 when rounded to the nearest hundredth.
