Statistical Methods

Unit 2 - Probability distributions

2.4.1.Examples
Example 2
Find the probability of getting only one catla in a sample of 10 fishes drawn one by one, if the probability of a catla being drawn in any draw is 0.2.
Answer
In a sample of size n, the probability getting x catla is given by,

For x = 0, 1, 2....................10
In this example p is the probability of a catla being drawn in any draw which is given to be 0.2,
i.e., p = 0.2
q = 1-p = 1-0.2 = 0.8
Sample size n = 10, x = 1, i.e., getting one catla
Probability of getting one catla is given by,

Example 3
What is the probability of finding 2 males in a sample of 5 fishes drawn one by one? (Assume sex ratio is 1:1).
Answer
The probability of finding male = 0.5 = p (say).
The probability of not finding male (i.e. finding female) 0.5 = q (say). Further n=5 and x=2.
Hence, the required probability using binomial distribution is given by,