Aaargh, jeg hater slike gåter med løsninger som er totalt uintuitive. Samtidig elsker jeg dem. Jeg har tidligere blogget om Monty Hall-problemet. Her kommer en ny gåte som også handler om sannsynlighetsberegning, noe vi mennesker er usedvanlig dårlig til rent intuitivt. Det er vel også mye av årsaken til at folk tror på mirakler og må forklare "umulige" hendelser med noe paranormalt...
Gåten har to ulike formuleringer:
1) Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
2) Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
Hva tror du?
Paradokset ble først beskrevet av Martin Gardener i Scientific American i 1959. Men noen tiår senere laget Marilyn Vos Savant, kvinnen som også er kjent fra Monty Hall-problemet, to nye varianter av gåtene. Først i 1991:
A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?
Og i 1996:
Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?
To andre varianter formulert i forbindelse med en undersøkelse utført i 2004 er:
Mr. Smith says: ‘I have two children and at least one of them is a boy.' Given this information, what is the probability that the other child is a boy?
Mr. Smith says: ‘I have two children and it is not the case that they are both girls.' Given this information, what is the probability that both children are boys?
Svaret er for øvrig omdiskutert og svært avhengig av hvordan spørsmålet ordlegges. For en grundig gjennomgang av paradokset og løsningene, kan du kose deg med gåtens Wikipedia-side.
