Ex 13.4, 12 - Chapter 13 Class 12 Probability

Transcript

Ex 13.4, 12 Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X). The first 6 positive integers are : 1, 2, 3, 4, 5, 6 Let X : be the larger number of two numbers selected The possible outcomes are Sample space = S = 1, 2 , 1, 3 , 1, 4 , 1, 5 , 1, 6 , 2, 1 , 2, 3 , 2, 4 , 2, 5 , 2, 6 , 3, 1 , 3, 2 , 3, 4 , 3, 5 , 3, 6 , 4, 1 , 4, 2 , 4, 3 , 4, 5 , 4, 6 , 5, 1 , 5, 2 , 5, 3 , 5, 4 , 5, 6 , 6, 1 , 6, 2 , 6, 3 , 6, 4 , 6, 5 Total number of possible outcomes = 30 The larger number can be : 2, 3, 4, 5 or 6 So, the values of X can be : 2, 3, 4, 5 or 6 Thus, the probability distribution is The mean Expected value is given by = = =1 = 2 2 30 +3 4 30 + 4 6 30 + 5 8 30 + 6 10 30 = 4 + 12 + 24 + 40 + 60 30 = 140 30 =