Mr.and Mrs.Jones have five children,all girls.
Mrs.Jones:I do hope our next child isn't another girl.
Mr.Jones:My dear,after five females,it's bound to be a boy.
Is Mr.Jones right?
Many gamblers think they can win at roulette by waiting until there is
a long run of red numbers,then betting on black. Will such a system work?
Edgar Allan Poe (大名鼎鼎的爱伦·坡,我有本他的文集,要借的来要哦.)argued that
if you roll five twos in a row, your chances of getting a two on the next
roll are less than one-sixth. Was he right?
If you answered yes to any of these questons, you have fallen into a trap
called the "gambler's fallacy".(赌徒的错误想法) In every case the next event
is completely independent of all previous events.(在所有的事例中,下一个事件与
之前的事件是完全独立的.)
The probability(概率),of Mr.and Mrs.Jones having a sixth girl is the same as
that of her first child having been a girl.The probability of the next roulette
number being red is the same as that of the previous number having been
red. The probability of a two on the next throw of the die(骰子) is still one-sixth.
To make this clearer,suppose Mr.Jones tosses five heads in a row with a fari
coin.(又是抛硬币) The chances of tossing heads again is exactly the same as
before:fifty-fifty.The coin has no memoy of what it did on previous flips.
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牢记概率论的两大原则: 等可能性原则以及独立性原则.(不懂的翻数学书去.)