If 2/11 is the probability that an even will happen, what is the probability that it will NOT occur?

1. Break Down the Problem

To find the probability that an event does not occur, we can utilize the complementary probability rule. This means that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.

2. Relevant Concepts

The complementary probability formula is given by: $P(\text{not } A) = 1 - P(A)$ where $P(A)$ is the probability of the event occurring.

3. Analysis and Detail

Here, we have:

• $P(A) = \frac{2}{11}$

Now, substituting this value into the complementary probability formula: $P(\text{not } A) = 1 - \frac{2}{11}$

Next, we'll convert 1 into the same denominator: $1 = \frac{11}{11}$

Thus, we can calculate: $P(\text{not } A) = \frac{11}{11} - \frac{2}{11} = \frac{11 - 2}{11} = \frac{9}{11}$

4. Verify and Summarize

The calculations show that we correctly applied the complementary probability formula. The probability that the event does not occur is calculated as follows: $P(\text{not } A) = \frac{9}{11}$

Final Answer

The probability that the event will NOT occur is $\frac{9}{11}$.