What Is Binomial Distribution?
Table Of Contents:
- What Is Binomial Distribution?
- Formula For Binomial Distribution.
- Diagram For Binomial Distribution.
- Examples Of Binomial Distribution.
(1) What Is Binomial Distribution?
- The Binomial Distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure.
- For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail.
- Binomial Distribution is the extension of Uniform Distribution because in Uniform Distribution you will do the experiment only once and calculate the probability.
- But in Binomial Distribution you can perform the ‘n’ number of experiments and calculate the probability of NUMBER OF TIMES Pass or Fail, True or False, 1 or 0 in that ‘n’ number of experiments.
- Suppose you are giving a competitive exam, you have 5 attempts to qualify for the exam.
- You can calculate the probability of passing the exam the first time.
- You can also calculate the probability of passing the exam 3 times using Binomial Distribution.
(2) Formula For Binomial Distribution?
(3) Diagram For Binomial Distribution?
- If you plot all the probability values of an experiment you will see the graph will come as symmetrical.
(4) Examples Of Binomial Distribution?
Example-1: Question
- Casino created a new game in which participants can place bets on the number of heads or tails in a specified number of coin flips.
- Assume a participant wants to place a $10 bet that there will be exactly six heads in 20 coin flips.
- The participant wants to calculate the probability of this occurring, and therefore, they use the calculation for binomial distribution.
Solution:
Here,
- n = 20 (Number Of Trials)
- x = 6 (Number Of Successful Trails)
- p = 0.5 (Probability Of Success In A Single Trail)
- Probability Of 6 Head = (20! / (6! × (20 – 6)!)) × (0.50)(6) × (1 – 0.50)(20 – 6)
- Probability Of 6 Head = 0.0369, or 3.7%.
Example-2: Question
- 60% of people who purchase sports cars are men.
- Find the probability that exactly 7 are men if 10 sports car owners are randomly selected.
Solution:
Here,
- n = 10 (Number Of Trials)
- x = 7 (Number Of Successful Trails)
- p = 0.6 (Probability Of Success In A Single Trail
