Probability And Binomial Distribution

Concept:
When objects are drawn without replacement, the probability of successive events changes after each draw. If the total number of objects is , and objects satisfy a condition, the probability can be computed using either:

• Multiplication rule of probability, or
• Combination formula

Step 1: Determine the total number of balls.

Step 2: Compute the probability using the multiplication rule.
Probability that the first ball is red: After drawing one red ball, remaining red balls and total balls . Probability that the second ball is red:
Step 3: Find the joint probability.

Concept:
A Normal distribution follows the well-known Empirical Rule (also called the 68–95–99.7 rule). This rule describes how data is distributed around the mean.

• About of the data lies within standard deviation of the mean.
• About of the data lies within standard deviations of the mean.
• About of the data lies within standard deviations of the mean.

Step 1: Identify the required interval.
The question asks for the percentage of data within two standard deviations from the mean.
Step 2: Apply the Empirical Rule.
According to the empirical rule:

Concept:
For a Poisson distribution with parameter :

• Mean
• Variance
• The third central moment is also equal to

Thus,
Step 1: Identify the parameter of the distribution.
The mean of the Poisson distribution is given as:
Step 2: Use the formula for the third central moment.
Substituting the value: