Respuesta :
Answer:
So, the probability is P=0.3087.
Step-by-step explanation:
We know that Priya's cat is pregnant with a litter of 5 kittens, so n=5.
Each kitten had a 30% chance of being chocolate brown.
We get that p=0.3 and q=1-0.3=0.7.
We calculate the probability that exactly 2 kittens will be chocolate brown, so k=2.
We use the formula:
[tex]\boxed{P(X=k)=C_k^n\cdot p^k\cdot q^{n-k}}[/tex]
we get
[tex]P(X=2)=C_2^5\cdot 0.3^2\cdot 0.7^3\\\\P(X=2)=\frac{5!}{2!(5-2)!}\cdot 0.03087\\\\P(X=2)=10\cdot 0.03087\\\\P(X=2)=0.3087\\[/tex]
So, the probability is P=0.3087.
The probability that exactly 2 kittens will be chocolate brown is 0.3087 and this can be determined by the given data.
Given :
- Priya's cat is pregnant with a litter of 5 kittens.
- Each kitten had a 30% chance of being chocolate brown.
The following steps can be used in order to determine the probability that exactly 2 kittens will be chocolate brown:
Step 1 - The formula of probability that can be used is given below:
[tex]\rm P(X=k) = \; ^nC_k \times p^k \times (1-p)^{n-k}[/tex]
Step 2 - According to the given data, the value of k is 2 and the value of p is 0.3.
Step 3 - Now, substitute the values of the known terms in the above expression in order to determine the probability that exactly 2 kittens will be chocolate brown.
[tex]\rm P(X=2) = \; ^5C_2 \times (0.3)^2 \times (1-0.3)^{5-2}[/tex]
[tex]\rm P(X=2) = \; ^5C_2 \times (0.3)^2 \times (0.7)^{3}[/tex]
Step 4 - Simplify the above expression.
P(X = 2) = 0.3087
For more information, refer to the link given below:
https://brainly.com/question/795909
