A batch of 25 batteries contains 6 that are defective. A of two are selected, at
ID: 3204986 • Letter: A
Question
A batch of 25 batteries contains 6 that are defective. A of two are selected, at random, without replacement from the batch. What is the probability that the second one selected is defective, given that the first one is defective? What is the probability that both are defective? What is the probability that the second one selected is defective? [use total probability rule] In a city, 51% of the adults are males. (It doesn't take too much advanced mathematics to deduce that the other 49% are females.) Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the US-Substance Abuse and Mental Health Services Administration) One adult is randomly selected: Find the probability that the selected person is a male. It is later learned that the selected survey subject was smoking a cigar. use the above information to find the probability that the selected subject is a male.[Bayes rule]Explanation / Answer
1:
(a)
The probability that first defective item is selected will be
P(first defective) = 6/25
After selecting the first one, there are 5 are remaining out of 24 so the probability of getting second defective is
P(second defective|first defective) = 5/24
(b)
The probability that both are defective is
P(second defective and first defective) = P(second defective|first defective)*P(first defective) = (6/25) * (5/24) = 0.05
(c)
P(first defective) = 6/25
P(second defective|first defective) = 5/24
And
P(first non defective) = 19/25
P(second defective|first non defective) = 6/24
By the law of total probability, the probability of second defective is
P(second defective) = P(second defective|first non defective)P(first non defective) + P(second defective|first defective) P(first defective) = (6/25) *(5/24) + (19/25) *(6/24) = 0.24
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