Question

1. a litter of kittens has one gray females, three gray males, two black females, and two black male. if you pick two kittens what is the probability that both are female?

Explanation:

Step1: Count total kittens

Total kittens = $1 + 3 + 2 + 2 = 8$

Step2: Count total female kittens

Total females = $1 + 2 = 3$

Step3: Calculate total 2-kitten combinations

Total ways = $\binom{8}{2} = \frac{8!}{2!(8-2)!} = \frac{8 \times 7}{2 \times 1} = 28$

Step4: Calculate female 2-kitten combinations

Female ways = $\binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2}{2 \times 1} = 3$

Step5: Compute probability

Probability = $\frac{\text{Female ways}}{\text{Total ways}} = \frac{3}{28}$

Answer:

$\frac{3}{28}$