Let the mean and variance of 7 observations 2,4,10, x, 12,14, y, x>y , be 8 and 16 respectively. Two numbers are chosen from 1,2,3, x-4, y, 5 one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :

Step-by-step solution

Mean = 8 gives x + y = 14 . Variance = 16 gives (x-8)^2 + (y-8)^2 = 4 . Solving: x = 8 , y = 6 (since x > y ). Set becomes 1, 2, 3, 4, 6, 5 = 1, 2, 3, 4, 5, 6 . Total ways to choose 2 numbers = 6 2 = 15 . Favorable cases (smaller Total favorable = 12. Probability = 12 15 = 4 5 .