Question

2. A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as "seconds." (a) Among six randomly selected goblets, how likely is it that only one is a second?

Answer 1

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 ;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x =0,1,2,3,....$

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) = $\binom{6}{1}0.10^{1}(1-0.10)^{6-1}$

               = $6*0.10 *0.90^{5}$ = 0.3543 or 35.43%

Therefore, among six randomly selected goblets, 35.43% it is likely that only one is a second.

Answer 2

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)

=$6C1(0.1)(0.5)^5\\= 0.01875$