Binomial Distribution
Maharashtra Board · Class 12 · Mathematics & Statistics
Quick revision notes for Binomial Distribution — Maharashtra Board Class 12 Mathematics & Statistics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Bernoulli Trials - Foundation Concepts
- A Bernoulli trial is an experiment with exactly two possible outcomes: success or failure
- Each trial must be independent of all other trials
- The probability of success (p) remains constant throughout all trials
Binomial Distribution Formula and Applications
- Binomial distribution gives probability of exactly x successes in n independent trials
- The formula comes from the binomial expansion of (q + p)^n
- Each term in the expansion represents probability of specific number of successes
Step-by-Step Problem Solving Techniques
- Step 1: Identify if the problem involves Bernoulli trials
- Step 2: Determine n (number of trials) and define success/failure
- Step 3: Calculate p (probability of success) and q = 1-p
Mean, Variance, and Standard Deviation
- Mean (Expected Value) of binomial distribution is simply n × p
- Variance measures spread of the distribution and equals n × p × q
- Standard deviation is the square root of variance
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