121- A company that produces fine crystal knows from experience that 10% of its

Question

121- A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as “seconds”

note:you need to figure out if this is a“combination” or “permutation” problem

a-Among six randomly selected goblets, how likely is it that only one is a second?

b-Among six randomly selected goblets, what is the probability that at least two are seconds?

c-If goblet are examined one by one, what is the probability that at most five must be selected to find four that are not seconds

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a.
P( X = 1 ) = ( 6 1 ) * ( 0.1^1) * ( 1 - 0.1 )^5
= 0.3543

b.
P( X < 2) = P(X=1) + P(X=0) +
= ( 6 1 ) * 0.1^1 * ( 1- 0.1 ) ^5 + ( 6 0 ) * 0.1^0 * ( 1- 0.1 ) ^6 +   
= 0.8857
P( X > = 2 ) = 1 - P( X < 2) = 0.1143

c.
P( X = 1 ) = ( 5 1 ) * ( 0.1^1) * ( 1 - 0.1 )^4
= 0.3281

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