Statistics > QUESTIONS & ANSWERS > Statistics questions and answers. Proved for A grades (All)

Statistics questions and answers. Proved for A grades

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Q.2 An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that they are all of the same color if: (5 marks ) (a) the balls are drawn witho... ut replacement; (b) the balls are drawn with replacement. Ans) a) There are 3 ways to have same color P(R) p(R) p(R) + p (b) p(b) p(b) + p(G) p(G) p(G) = [(5/19)*(4/18)*(3/17)] + [(6/19)*(5/18)*(4/17)]+ [(8/19)*(7/18)*(6/17)] = 516/5814 b) There are 3 ways to have same color P(R) p(R) p(R) + p (b) p(b) p(b) + p(G) p(G) p(G) = (5/19)3 + (6/19)3 + (8/19)3 = 853/6859 Q.3 Find the probability mass function and the cumulative distribution function for getting 3 when the dice are thrown.(5 marks) The possibilities for getting face 3 are no ‘3’ , one ‘3’ and two ‘3’s Therefore P( no ‘3’) = 25/36, p( one 3) = 10/36 p( two 3) = 1/36 F(x) = ∑ p( X < x) F (0) = p(0) = 25/36 F(1) = p(0) + p(1) = 25/36 + 10/36 = 35/36 F(2) = p(2) + F(1) = 1/36 + 35/36 = 1 [Show More]

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