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In drawing a sample of size n under SRSWR from a population of size N, the probability that a specified member is included in the chosen sample is

This question was previously asked in
SSC CGL Tier-II ( JSO ) 2016 Official Paper ( Held On : 2 Dec 2016 )
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  1. \(\dfrac{1}{N}\)
  2. \(\dfrac{n}{N}\)
  3. \(1-\left(1-\dfrac{1}{N}\right)^n\)
  4. \(\dfrac{(N-1)^n}{N^n}\)

Answer (Detailed Solution Below)

Option 3 : \(1-\left(1-\dfrac{1}{N}\right)^n\)
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Detailed Solution

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Explanation

The probability of selecting the specified member from a population size of N will be 1/N

∴ The probability of not selecting the specified member = 1- 1/N

⇒ (N – 1)N

∴ The probability of not including the specified member in the choosen sample = (1 – 1/N)n

∴ The probability of always including the specified member in the specified sample is 1 – (1 – 1/N)n

The simple random sampling with replacement = It is called SRSWR, in it a unit is selected from the sampling framE. The unit is replaced back and the next unit is selected. This process is repeated till a sample of the desired size is selected.

When n units are selected with SRSWR, the total number of possible samples are Nn

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