An unbiased die is tossed 500 times. What is the mean of the number of ‘sixes’ in these 500 tosses?

Solution:

The given random experiment is a Bernoulli’s trial with 500 independent trials with success as getting six.

Here, ‘p’ denotes the probability of success then p = 1/6 and ‘q’ denotes probability of failure (not getting six) then q = 1 - 1/6 = 5/6

Now we have a mean of binomial distribution of ‘n’ Bernoulli’s trials is given by ‘np’.

Now, number of trials = n = 500 

∴ mean of the number of ‘sixes’ = np = 500 × 1/6 = 500/6 

Example: Under the same random experiment find variance and standard deviation.

Solution: The variance of binomial distribution is = npq = 500 × 1 / 6 × 5 / 6 = 2500 / 36

Standard deviation = √(npq) = √(2500 / 36) = 50 / 6

An unbiased die is tossed 500 times. What is the mean of the number of ‘sixes’ in these 500 tosses?

Summary:

The mean of the number of ‘sixes’ of an unbiased die for 500 tosses is 500 / 6.