Problem 15 A family has three children A B and C of height X

Problem 15. A family has three children, A, B, and C, of height X1, X2. X3. respectively. If X1, X2, X3 are independent and identically distributed continuous random variables, evaluate the following probabilities: (a) P(A is the tallest child). (b) P(A is taller than B I A is taller than C). (c) P(A is taller than B I B is taller than C). (d) P(A is taller than B I A is shorter than C). (e) P(A is taller than B B is shorter than C).

Solution

a) P(A is tallest) = 1/3 = 0.333

b) P(A is taller than B/A is taller than C ) = 1/2 =0.5

c) P(A is taller than B/B is taller than C ) = 1/2 =0.5

d) P(A is taller than B/A is shorter than C ) = 1/2 =0.5

e) P(A is taller than B/B is shorter than C )=0.5