Binomial Distribution is the probability distribution of number of successes in

`n`

number of events (trials). For instance a die is thrown randomly 10 times, what's the probability of a five on rolling die in 7 out of 10 times? Here probability of a five `(p)`

is (1/6) on a single throw as die has six sides. `n`

is the the number of times die is thrown which is 10. `k`

is the number of times we want success which is 7.Solution

P(X < ) means probability of less than successes. Similarly P(X > ) refers to probability of more than successes.

How to calculate

To calculate P(X < ), we need to sum all the probabilities from P(X = 0) through
P(X = ). See the details below.
`P(X < ) `

How to calculate

To calculate P(X > ), we need to sum all the probabilities from P(X = ) through P(X = ). See the details below.
Binomial Distribution Table
`P(X > ) `

The sum of all the probabilities shown below will be 1.

Important Points

- Probability of success must lie between 0 and 1.
- Number of trials can't be less than or equal to 0. It must be a whole number, can't be in decimals.
- Number of successes can't be greater than the number of trials.

FAQs

Binomial Distribution has the following properties -

- Each trial has only two possible outcomes - success or failure.
- The probability of a success on any trial would be same.
- No trials depend on each other.

There is no specific definition of `success`

. You can define it as a desired outcome. It depends on the problem statement. See the examples below -

- If you flip a coin 10 times, what is the probability of getting more than four tails? Here "success" is getting tail.
- Suppose you play a video game (let's say mario). What is the probability that you win 3 of the 10 times. Here "success" is winning the game.
- Suppose school administation wants to know the number of students who take out their names from the randomly selected statistics class. The participation rate in the statistics class is 40% for any given school session. It means withdrawal rate is 60% i.e (1-0.4). Here "success" is a student who took out his/her name.