l****y
发帖数: 92 | 1 1/4 of married couples has no children at all. The other 3/4 of families
have exactly three children with equally likely to be boy or girl. What is
the probability that the male line of descent of a particular husband will
eventually die out?
谁能给个答案或者hint啊? | J****x
发帖数: 37 | 2 P = 1/4 + 3/4 * 1/2 * 1/4 + 3/4 * 1/2 * 3/4 * 1/2 * 1/4 + ...
= 1/4 * (1 + 3/8 + (3/8)^2 + (3/8)^3 + ...)
= 1/4 * 1/(1 - 3/8)
= 2/5 | l****y
发帖数: 92 | | J****x
发帖数: 37 | 4 Yes, I overlooked this condition. Sorry about that. In this case, we only
need to replace 1/2 with 1/8. Now, the result becomes:
P = 1/4 + 3/4 * 1/8 * 1/4 + 3/4 * 1/8 * 3/4 * 1/8 * 1/4 + ...
= 1/4 * (1 + 3/32 + (3/32)^2 + (3/32)^3 + ...)
= 1/4 * 1/(1 - 3/32)
= 8/29 | b********e
发帖数: 41 | 5 You cannot simply replace 1/2 with 1/8, bacause you can have 3 girls, 2g&1b,
1g&2b and 3boys, with probabilty 1/8, 3/8, 3/8 an 1/8.
Any couple have a 1/4 chance to have no children, that's 1/4.
And they have 3/4 chance to have 3 children, the chance that all of them are
girls is 3/4*1/8=3/32.
So the probabilty should be at least 1/4+3/32=11/32 which is > 8/29.
I got a numerical answer, 0.77, which is pretty large, but I think is
possible. | l****y
发帖数: 92 | 6 thanks, 0.77 is the right answer! | s******f
发帖数: 89 | 7 well, this implies
p=1/4+3/4*1/8+3/4*(3/8*p+3/8*p^2+1/8*p^3)
=> p=0.77
1b,
are
【在 b********e 的大作中提到】
: You cannot simply replace 1/2 with 1/8, bacause you can have 3 girls, 2g&1b,
: 1g&2b and 3boys, with probabilty 1/8, 3/8, 3/8 an 1/8.
: Any couple have a 1/4 chance to have no children, that's 1/4.
: And they have 3/4 chance to have 3 children, the chance that all of them are
: girls is 3/4*1/8=3/32.
: So the probabilty should be at least 1/4+3/32=11/32 which is > 8/29.
: I got a numerical answer, 0.77, which is pretty large, but I think is
: possible.
| J****x
发帖数: 37 | 8 Bluechange, I am assuming having three girls does not terminate the process,
since daughters may still have grandsons. In this case, I think my answer
is correct.
If we assume the male descent line vanishes either the couple have three
daughters or they have no childen, you answer is correct. My solution is as
follows.
Let P the target probability. Consider the following cases for a given
couple:
1. 1/4 chance they have no children, the processes terminates.
2. 3/4 * 1/8 chance, they have three | b********e
发帖数: 41 | 9 Now this is a social problem, a girl's son doesn't carry the y part of the
girl's father's sex chromosome, but he does carry some part of the girl's
father's other chromosomes. Then what is a descent?
Who knows. |
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