Find an equation of the plane that passes through the point and contains the line

(a) 0.8649

(b) 0.6469

(c) 0.353

Step-by-step explanation:

We are given that a diamond can be classified as either gem dash quality or industrial dash grade. Suppose that 93% of diamonds are classified as industrial dash grade.

(a) Two diamonds are chosen at random.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 2 diamonds

            r = number of success = both 2

           p = probability of success which in our question is % of diamonds

                  that are classified as industrial dash grade, i.e; 0.93

LET X = Number of diamonds that are industrial dash grade

So, it means X ~

Now, Probability that both diamonds are industrial dash grade is given by = P(X = 2)

       P(X = 2)  =

                      =

                      = 0.8649

(b) Six diamonds are chosen at random.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 6 diamonds

            r = number of success = all 6

           p = probability of success which in our question is % of diamonds

                  that are classified as industrial dash grade, i.e; 0.93

LET X = Number of diamonds that are industrial dash grade

So, it means X ~

Now, Probability that all six diamonds are industrial dash grade is given by = P(X = 6)

       P(X = 6)  =

                      =

                      = 0.6469

(c) Here, also 6 diamonds are chosen at random.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 6 diamonds

            r = number of success = at least one

           p = probability of success which is now the % of diamonds

                  that are classified as gem dash quality, i.e; p = (1 - 0.93) = 0.07

LET X = Number of diamonds that are of gem dash quality

So, it means X ~

Now, Probability that at least one of six randomly selected diamonds is gem dash quality is given by = P(X 1)

       P(X 1)  = 1 - P(X = 0)

                      =  

                      =

                      = 1 - = 0.353

Here, the probability that at least one of six randomly selected diamonds is gem dash quality is 0.353 or 35.3%.

For any event to be unusual it's probability is very less such that of less than 5%. Since here the probability is 35.3% which is way higher than 5%.

So, it is not unusual that at least one of six randomly selected diamonds is gem dash quality.