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Answer:
The probability that of the two chips selected both are defective is 0.1089.
Step-by-step explanation:
Let <em>X</em> = number of defective chips.
It is provided that there are 2 defective chips among 6 chips.
The probability of selecting a defective chip is:
A sample of <em>n</em> = 2 chips are selected.
The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> = 2 and <em>p</em> = 0.33.
The probability function of a Binomial distribution is:
Compute the probability that of the two chips selected both are defective as follows:
Thus, the probability that of the two chips selected both are defective is 0.1089.
The sample space of selecting two chips is:
S = (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5)