Then Xi are independent and have the same distribution as X: Since the number of boys per family in the second village is 1; the boy/girl ratio of second village is Pn 1 1 Pni=1 = Pn Xi i=1 i=1 Xi n Using the law of large numbers (which we’ learn soon), the ratio converges to ll
1
almost surely.
(c) 11 cards, one letter on each, compose the word "probability". Now randomly pick 7 cards one by one and without replacement. What is the probability that the 7 letters on the 7 cards sequentially form the word "ability"? What is the probability that the 7 cards can be used (by reordering) to form the word "ability". Answer: (i) In total there are "ability", there are
11! (11 7)!
possible ordered sequences of the 7 cards, and for the them to be 1 2 2 1 (2 1) 1 1 = 4
possible cases, thus the probability is
4 4!