Question

Find the probability that in 200 tosses of a fair six sided die, a five will be obtained at least 40 times

Answer 1

Since the no of trails are very large hence we assume it as Normal distribution to calculate probability as

n = number of trials = 200
p = probability of getting a five in one trail = 1/6=0.1667

Since, n*p = 200(1/6) = 33.333

also, n*(1-p) = 166.667 both are greater than 10 hence Normal distribution assumption is correct.

Now, mean = np = 33.33 also,

Standard deviation, s = sqrt(np(1-p)) = sqrt(200(1/6)(5/6)) = 5.27

Now for correction we will use 39.5 instead of X=40 because the question is at least 40 which means 40 has to be included.

Now, Z

Hence using Z table shown below,  area above Z=1.27 is

=0.121.