Respuesta :
Answer:
0.24% probability that all 5 bags selected are defective
Step-by-step explanation:
For each bag, there are only two possible outcomes. Either they are defective, or they are not. The probability of a bag being defective is independent from other bags. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
30% of the plastic bags produced are defective
This means that [tex]p = 0.3[/tex]
A sample of 5 plastic bags is selected at random
This means that [tex]n = 5[/tex]
What is the probability that all 5 bags selected are defective?
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.0024[/tex]
0.24% probability that all 5 bags selected are defective
