Uploaded October 2013 | Updated September 2026, 2 hours ago
An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at statcan.gc.ca/pub/84-537-x/4064441-eng.htm. The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932
An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at statcan.gc.ca/pub/84-537-x/4064441-eng.htm. The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932
