Respuesta :
Answer:
0.3019
Step-by-step explanation:
Let the total number of toasters in a carton (n) = 10
It is also said that there is a possibility that one of the toaster will be sent back for repair is 20%
∴ if p = 0.2 and p + q = 1
It means that q = 1 -p
q = 1 - 0.2
q = 0.8
If we represent the A to be the number of coaster that need repair, The probability that exactly 2 coasters will need repair is required to be calculated.
Also, Let b = 2
From the foregoing, a binomial model is best fit to solve this problem.
Given that n= 10 and p = 0.20
To find P(A = 2); we have :
P(A = 2) = [tex]_{n}C_b(p)^2(q)^{n-b}[/tex]
P(A = 2) = [tex]_{10}C_2(0.2)^2(0.8)^{10-2}[/tex]
P(A = 2) = [tex]\frac{10!}{2!(10-2)!} (0.2)^2(0.8)^8[/tex]
P(A = 2) = [tex]\frac{10!}{2!(8)!} (0.2)^2(0.8)^8[/tex]
P(A = 2) = [tex]\frac{10*9*8!}{2!(8)!} (0.04)(0.1677)[/tex]
P(A = 2) = [tex]\frac{10*9}{2} (0.04)(0.1677)[/tex]
P(A = 2) = 45 × (0.04) × (0.1677)
P(A = 2) = 0.30186
P(A = 2) = 0.3019 (to four decimal places)
The probability that in a carton, there will be exactly 2 toasters that need repair is; 0.3019
How to solve binomial probability problem?
We are told that there is a 20% chance that any one of the toasters will need to be sent back for minor repairs. Thus;
p = 20% = 0.2
q = 1 - p
q = 1 - 0.2
q = 0.8
We want to find the probability that in a carton, there will be exactly 2 toasters that need repair.
We can solve that using binomial probability formula;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
We have; n= 10 and p = 0.20
Thus;
P(X = 2) = 10C2 * 0.2² × 0.8^(10 - 2)
Using online binomial probability calculator, we have;
P(X = 2) = 0.3019
Read more about binomial probability at; https://brainly.com/question/15246027
