Problem: denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination .
Rationale: when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 39263999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well . we ' ll get 3925 / 4000 = 157 / 160 . answer : c .
annotated_formula: divide(subtract(4000, 75), 4000)