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?

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)

=

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for