Question

A fair die is rolled 1000 times. Let A be the event that the number of...

A fair die is rolled 1000 times. Let A be the event that the number of 6’s is in the interval[150,200], and B the event that the number of 5’s is exactly 200. (a) Approximate P(A).(b) Approximate P(A|B).

Homework Answers

Answer #1
n= 1000 p=probability of a number= 1/6
here mean of distribution=μ=np= 166.67
and standard deviation σ=sqrt(np(1-p))= 11.79
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

a)

P(A) =P(149.5<X<200.5)=P((149.5-166.67)/11.785)<Z<(200.5-166.67)/11.785)=P(-1.46<Z<2.87)=0.9979-0.0721=0.9258

b)

n= 800 p(A|B)=probability of 5 given 6 is not in them=1/5= 0.20
here mean of distribution=μ=np= 160.00
and standard deviation σ=sqrt(np(1-p))= 11.31
probability =P(199.5<X<200.5)=P((199.5-160)/11.314)<Z<(200.5-160)/11.314)=P(3.49<Z<3.58)=0.9998-0.9997=0.0001


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