The binomial distribution

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

Coin flipping

Hand flipping coin with one side H with 50% chance, other side T with 50% chance.png

H and T, 1 and 0, Success and Failure, Win and Loss.png

Probability distribution of the number of successes in a sequence of independent events
For example, the number of heads in a sequence of coin flips
Described by $n$ and $p$
- $n$: total number of events
- $p$: probability of success

Plot of binomial distribution with n=10, p=0.5.png

binomial_distribution_with_successes_less_than_or_equal_to_7_highlighted_probability_equals_99_point_four_five_percent.png

normal_distribution_shaded_blue_for_successes_above_seven_equal_to_five_point_five_five_percent.png

${Expected \ value} = n \times p$

Expected number of heads out of 10 flips $= 10 \times 0.5 = 5$

If we don't know $p$, but know $n$ and the expected value:

${p} = \frac{expected \ value}{n} $

The binomial distribution is a probability distribution of the number of successes in a sequence of independent events

Box of tickets with three zeros and three ones. 50% chance of zero, 50% chance of one.png

The binomial distribution is a probability distribution of the number of successes in a sequence of independent events

Probabilities of second event are altered due to outcome of the first

If events are not independent, the binomial distribution does not apply!

Box of tickets with three zeros and two ones. 60% chance of zero, 40% chance of one.png

The binomial distribution can be used for independent events producing binary outcomes

¹ Image credit: https://unsplash.com/@towfiqu999999

Introduction to Statistics