Respuesta :
Answer:
0.01875
Step-by-step explanation:
Given that a company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as "seconds."
Let X be the no of seconds.
For any randomly drawn crystal to be as second has a probability 0.10
and this probability is constant for any draw as each crystal is independent of the other
Hence X no of seconds in the sample of 6 goblets is Binomial with n =6 and p = 0.10
Required probability = P(x=1)
=[tex]6C1(0.1)(0.5)^5\\= 0.01875[/tex]
Answer:
Probability that among six randomly selected goblets, only one is a second = 35.43% .
Step-by-step explanation:
We are given that a company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as "seconds".
This situation can be represented as Binomial distribution ;
[tex]P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x =0,1,2,3,....[/tex]
where, n = number of trials (samples) taken = 6
r = number of success = 1
p = probability of success which is % of goblets that have been
classified as "seconds" , i.e.; 10%
Let X = No. of goblets having cosmetic flaws and must be classified as "seconds".
So, Probability that among six randomly selected goblets, only one is a second = P(X = 1)
P(X = 1) = [tex]\binom{6}{1}0.10^{1}(1-0.10)^{6-1}[/tex]
= [tex]6*0.10 *0.90^{5}[/tex] = 0.3543 or 35.43%
Therefore, among six randomly selected goblets, 35.43% it is likely that only one is a second.
