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1. Chapter 13 Class 12 Probability
2. Serial order wise
3. Ex 13.4

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 And they are selected without replacement 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 𝝁=𝑬(𝑿)=∑_(𝑖=1)^𝑛▒𝑥𝑖𝑃𝑖 = 2 × 2/30+"3 × " 4/30+ 4 × 6/30+ 5 × 8/30+ 6 × 10/30 = (4 + 12 + 24 + 40 + 60)/30 = 140/30 = 𝟏𝟒/𝟑

Ex 13.4 