The probability that an event will happen is

Upper P left parenthesis Upper E right parenthesisP(E)equals=StartFraction 22 Over 31 EndFraction2231.

Find the probability that the event will not happen.

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Part 1

The probability that the event will not happen is

enter your response here.

​(Type an integer or a simplified​ fraction.)

The probability that an event will not happen is the complement of the probability that the event will happen. If the probability of event \( E \) happening is \( P(E) \), then the probability that event \( E \) will not happen is given by:

\[
P(\text{not } E) = 1 - P(E)
\]

Given \( P(E) = \frac{22}{31} \), the probability that the event will not happen is:

\[
P(\text{not } E) = 1 - \frac{22}{31}
\]

We subtract the fractions:

\[
P(\text{not } E) = \frac{31}{31} - \frac{22}{31} = \frac{31 - 22}{31} = \frac{9}{31}
\]

Thus, the probability that the event will not happen is:

\[
\boxed{\frac{9}{31}}
\]

Would you like more details or further clarifications?

Here are 5 related questions for practice:
1. If \( P(E) = \frac{5}{8} \), what is \( P(\text{not } E) \)?
2. If the probability of an event not happening is \( \frac{7}{15} \), what is the probability that it will happen?
3. If an event is certain to happen, what is the probability that it will not happen?
4. If the probability of an event happening is \( 0.6 \), what is the probability that it will not happen?
5. What is the relationship between complementary probabilities?

**Tip:** The sum of the probabilities of an event happening and not happening always equals 1.

The probability that an event will happen is P(E) = 22/31. Find the probability that the event will not happen. (Type an integer or a simplified fraction.)

Learn how to calculate the probability of an event not happening when P(E) = 22/31. This problem focuses on the concept of complementary probabilities and how to apply the formula P(not E) = 1 - P(E). Suitable for students in Grades 6-8.

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