An urn contains 10 red balls, 5 blue balls and 15 green balls. Five balls are drawn with replacement.Use simulation (>2000 trials)to answer the following questions: (20 pt)

1. What is the probability of drawing a total of 2 red and 3 green balls ?

2. What is the probability of drawing 5 blue balls ?

3. Compare your answers in (1) and (2) with the theoretical answers.(Recall that The multinomial distribution says that given probabilities p1 for event 1, p2 for event 2, ...pk for event k, if N observations are made independently and at random, then the probability of getting exactly n1 of kind 1, n2 of kind 2...and nk ofkind K where n1+n2+....+nk = Nis: N!/(n1! n2!....nK!) * p1^n1 *p2^n2*....p^kn. Note that p1^n1indicates raising p1 to the power n1 etc. Note also that if you use it,the Excel function multinomial (n1,n2,...nK) calculates only the first part of the above expression namely N!/(n1! n2!....nK!). )

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