Question

hello thank you for viewing my question I seem to be stuck on this problem can you please help thank you

Answer 1

We have 9 boy kittens and 6 girl kittens, a total of 15 kittens.

9 cats will be selected and we have to calculate the probability that 5 boy kitttens and 4 girl kittens are chosen.

We could have modeled as a binomial experiment, but the probability of choosing a boy kitten is not constant after each selection. Then, we have to select an alternative method.

We can think of it of a combinatorial problem.

In this case, it is a combination problem, as the order of selection does not matter and each kitten is equivalent within its category.

Repetition is not allowed: a kitten selected can not be selected again.

We can start finding all the possible combinations for 9 kittens out of the total 15 kittens:

`C(15,9)=(15!)/(9!(15-9)!)=(15!)/(9!6!)=5005`

The probability of selecting 5 boys and 4 girls will be the relation between the outcomes where there are 5 boys and 4 girls and the total number of outcomes we have just calculated.

Then, we can now calculate how many combinations of 9 kittens have 5 boys and 4 girls as a product of two combinations: the combinations for the boys C(9;5) and the combinations for the girls C(6;4).

We can calculate this as:

`\begin{gathered} C(9,5)=(9!)/(5!4!)=126 \\ C(6,4)=(6!)/(4!2!)=15 \\ =>C(9,5)*C(6,4)=126*15=1890 \end{gathered}`

We can now calculate the probability as the ratio of combinations 1890/5005:

`p=(1890)/(5005)\approx0.378`

Answer: the probability is 0.378.