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Answer:
(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.
(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.
(c) The probability that at most five must be selected to find four that are not seconds is 0.9453.
Step-by-step explanation:
Let <em>X</em> = number of seconds in the batch.
The probability of the random variable <em>X</em> is, <em>p</em> = 0.31.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is:
(a)
Compute the probability that only one goblet is a second among six randomly selected goblets as follows:
Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.
(b)
Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:
P (X ≥ 2) = 1 - P (X < 2)
Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.
(c)
If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.
P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)
Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.