Final answer:
The probability that exactly 6 out of 10 kittens are female, assuming equal likelihood of male and female births, is best calculated using the binomial probability formula. The answer, rounded to three decimal places, is approximately 0.210, which corresponds to option (a).
Step-by-step explanation:
The subject of this question is Probability, which falls under the branch of Mathematics. The student is inquiring about finding the chance of a specific event happening, given the assumption that male and female kitten births are equally likely. The event in question is that exactly 6 out of 10 kittens are female.
To calculate this probability, we use the binomial probability formula:
Probability(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Here, n represents the total number of kittens (10), k is the number of female kittens we want to have (6), and p is the probability of one kitten being female (0.5 since births are equally likely to be male or female).
Using the formula, we can calculate the probability:
= (10 choose 6) * (0.5)^6 * (0.5)^(10-6)
= 210 * (0.5)^6 * (0.5)^4
= 210 * (0.5)^10
= 210 * (0.0009765625)
= 0.205078125
The answer that is closest to our calculation is (a) 0.210.