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Let’s go right back to the first example in this chapter:

Let’s say you have a single six-sided die. If you role it, what is the probability you will roll a 1?

If you remember, the answer was 1/6.

Now let’s put some money on this. You’re in Vegas, and you’re going to win $500 if the die lands on 1. When it does, you just won $500! Let’s call that a success. You had a 1/6 chance to achieve that success.

But you decide to let it ride! You’re convinced it can happen again. You go double or nothing, betting again on 1. This time, the die comes up on something else! You’ve failed. And since 5 out of the 6 outcomes would have caused that failure, the probability to fail is 5/6.

Now, let’s turn it around. What if someone were to offer you $500 if, when you roll one die, you rolled at least a 2? Think about that for a second. What outcome would win you $500? If you’re just thinking of 2, think again. In fact, if you rolled a 2, or a 3, or a 4, or a 5, or a 6, you would win! That’s pretty good. What are the odds of that happening? You could figure out that there are 5 ways to win out of 6, so the answer would be 5/6. The probability of success would be 5/6.

But, by using the phrase “at least,” the problem created more ways to succeed than to fail. That means more work. On the GMAT, we want to avoid hard work. Try to figure out how you could fail, and then reverse it? The only way NOT to win $500 is to roll a 1. And what’s the probability that you’d roll a 1? 1/6. The probability of failure is 1/6, so the probability of success must be 5/6.

To simplify it, look at this formula:

P(success) + P(failure) = 1
or
P(success) = 1 – P(failure)

Example 15

Chapter 5: A Different Method