Question

(About Moivre Laplace theorem in probability theory). Two dice are rolled 4400 times. Find out probability that exactly in 350 cases the sum on the two dice will not be less than 11.

Answer 1

On rolling a pair of dice ,

P( sum of dice not less than 11 ) = 3/36 =1/12

Possible cases are (5,6)(6,5) and (6,6)

Now ,for normal approximation (also called moivre laplace theorem ) of binomial probabililty, we have

n= 4400

p= 1/12

q=1-p = 11/12

Mean = n*p =4400/12 = 366.67

Std dev = sqrt(n*p*q) = 18.33

Using normal distribution probability,

Probability of having exactly 350 of such cases = 0

Beacause normal distribution is a continous diatribution ,hence only the probability that X Is greater or smaller than a partivular value can be found.