Final answer:
Angela had a total of six new kittens. For the hypothetical scenario at the Humane Society with nine kittens, calculations would need to be made based on the composition of the litter and the notion of selection without replacement to determine the probabilities of various outcomes.
Step-by-step explanation:
The student's question involves a basic count of kittens that resulted from a female cat giving birth. Originally Angela had a pair of cats. If the female gave birth to six kittens, three males and three females, the total number of new kittens Angela has is six (option a).
Addressing the other parts of the question, if we consider a litter at the Humane Society consisting of four tabby kittens and five black kittens, and a family randomly selects two kittens without replacement, we can then calculate probabilities for various scenarios.
- Probability that both kittens are tabby: There are 4 tabby kittens out of a total of 9. The probability of selecting one tabby kitten is 4/9. Without replacement, if one tabby is already chosen, there are now 3 tabby kittens and 8 total kittens left, making the probability of selecting another tabby 3/8. The combined probability for both events is (4/9) * (3/8).
- Probability of one kitten of each coloring: The probability for selecting one tabby and then one black kitten is (4/9) for the first tabby and (5/8) for the subsequent black kitten, since one kitten has already been taken. Conversely, it could also be (5/9) for the first black and then (4/8) for the tabby if the black is selected first.
- Probability a tabby is chosen as the second kitten when a black kitten was chosen first: If a black kitten has been chosen, we now have 4/8 or 1/2 chance of selecting a tabby.
- Probability of choosing two kittens of the same color: This could be the probability of choosing two tabbies or two black kittens. Both require multiplying two conditional probabilities like the ones we calculated for the tabbies.