In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. 8 of the dogs and 6 of the cats are male.

If two animals are selected at random, what is the probability that both are female cats?

42 animals

18-6 = 12 female cats
prob of female cat = 12/42

now we have 41 animals, 11 females cats
prob of female cat = 11/41

so
12/42 * 11/41

To find the probability that both selected animals are female cats, we need to determine the total number of animals and the number of female cats.

We are given that there are 24 dogs and 18 cats available for adoption. Out of these, 8 dogs and 6 cats are male, so we have 24 - 8 = 16 female dogs and 18 - 6 = 12 female cats.

To calculate the probability, we divide the number of favorable outcomes (two female cats) by the total number of possible outcomes (any two animals):

Total number of possible outcomes = total number of animals * (total number of animals - 1)

Total number of animals = number of dogs + number of cats = 24 + 18 = 42

Total number of possible outcomes = 42 * (42 - 1) = 42 * 41 = 1,722

Number of favorable outcomes = number of female cats * (number of female cats - 1)

Number of favorable outcomes = 12 * (12 - 1) = 12 * 11 = 132

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 132 / 1,722
Probability ≈ 0.0767 or 7.67%

Therefore, the probability of randomly selecting two animals and both being female cats is approximately 0.0767 or 7.67%.