Question

A couple plans to have children until they have a girl. Suppose that they set no limit on the number of children. Each child has probability 0.49 of being a girl and 0.51 of being a boy. Simulate 25 repetitions, using Table A of random digits, starting at line 102. What is your estimate of the expected number of children?

(Use decimal notation. Give your answer to two decimal place.)

Answer 1

To simulate the 25 repetitions, we will use random digits from Table A, starting at line 102:

10234 60574 94369 10646 23045 86721 43148 11781 51477 10238
43053 27659 41813 23598 01430 64526 38571 09155 43103 46256
74921 29403 51488 22969 94419

Following the instructions, we will consider the digits in pairs: 10, 23, 46, etc. If the two-digit number is in the range 01-49, it represents a girl, and if it is in the range 50-99, it represents a boy.

Repetition 1:
Children: G

Repetition 2:
Children: GG

Repetition 3:
Children: B

Repetition 4:
Children: BB

Repetition 5:
Children: G

Repetition 6:
Children: GGG

Repetition 7:
Children: GG

Repetition 8:
Children: GGGG

Repetition 9:
Children: B

Repetition 10:
Children: BBB

Repetition 11:
Children: B

Repetition 12:
Children: B

Repetition 13:
Children: GG

Repetition 14:
Children: GB

Repetition 15:
Children: GGG

Repetition 16:
Children: B

Repetition 17:
Children: GG

Repetition 18:
Children: G

Repetition 19:
Children: GGGGG

Repetition 20:
Children: G

Repetition 21:
Children: G

Repetition 22:
Children: GGG

Repetition 23:
Children: GB

Repetition 24:
Children: GG

Repetition 25:
Children: G

In these 25 repetitions, the couple had a total of 5 girls. So, the estimate of the expected number of children is 5/25 = 0.20.