Probability Walkthrough

Working a probability problem means identifying which rule the situation calls for before any arithmetic happens, because the rules differ by whether events overlap and whether one changes the odds of the next.

Three problems. First: two cards drawn from a deck without replacement — what is the chance both are aces? The draws are dependent, since removing an ace changes the second draw, so the conjunction rule uses a revised second figure. Four in fifty-two, then three in fifty-one, giving twelve in two thousand six hundred and fifty-two, about four tenths of one percent. Second: one card drawn — what is the chance it is a heart or a face card? These overlap, since three cards are both, so the disjunction rule subtracts the overlap once. Thirteen plus twelve minus three, over fifty-two: twenty-two in fifty-two, about forty-two percent. Third: four rolls of a die — what is the chance of at least one six? Computing that directly means adding four messy cases, so take the complement instead. The chance of no six on a roll is five in six, and across four rolls that is about forty-eight percent, leaving about fifty-two percent.