What is the complementary probability of rolling a 2 on a six-sided die?

The complementary probability of rolling a 2 on a six-sided die is 5/6.

When we talk about complementary probability, we mean the probability that the event does not happen. In this case, the event is rolling a 2 on a six-sided die. A standard six-sided die has six faces, each showing a different number from 1 to 6. The probability of rolling any specific number, such as a 2, is 1 out of 6, or 1/6.

To find the complementary probability, we need to calculate the probability of not rolling a 2. Since there are six possible outcomes when you roll the die, and only one of those outcomes is a 2, there are five outcomes that are not a 2. These outcomes are rolling a 1, 3, 4, 5, or 6.

The probability of not rolling a 2 is therefore the number of favourable outcomes (not rolling a 2) divided by the total number of possible outcomes (rolling the die). This gives us 5/6.

In summary, the complementary probability is simply 1 minus the probability of the event happening. So, if the probability of rolling a 2 is 1/6, the complementary probability is 1 - 1/6, which equals 5/6. This means that if you roll a six-sided die, there is a 5/6 chance that you will not roll a 2.