Fill in the blanks so that the resulting statement is true.

Because 

​P(E)plus+​P(not 

​E)equals=​1, 

then​ P(not 

​E)equals=​_______ 

and 

​P(E)equals=​_______.

Question content area bottom

Part 1

Because 

​P(E)plus+​P(not 

​E)equals=​1, 

then​ P(not 

​E)equals=

▼
 
1 minus Upper P left parenthesis not Upper E right parenthesis1−P(not E)

1 minus Upper P left parenthesis Upper E right parenthesis1−P(E)
 
and 

​P(E)equals=

▼
 
1 minus Upper P left parenthesis Upper E right parenthesis .1−P(E).

1 minus Upper P left parenthesis not Upper E right parenthesis .

Given the relationship:

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

This equation states that the probability of event \( E \) plus the probability of the event not \( E \) (i.e., the complement of \( E \)) is equal to 1.

To fill in the blanks:

- **\( P(\text{not } E) \) equals \( 1 - P(E) \)** because the probability of the complement of an event is \( 1 \) minus the probability of the event itself.

- **\( P(E) \) equals \( 1 - P(\text{not } E) \)** because the probability of the event is \( 1 \) minus the probability of its complement.

Thus, the completed statement is:

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

Would you like any further explanation or details on this topic?

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Here are five related questions to explore this concept further:

1. What is the probability of the complement of an event if \( P(E) = 0.7 \)?
2. If \( P(\text{not } E) = 0.4 \), what is \( P(E) \)?
3. How would you interpret \( P(E) = 0.8 \) in a real-world context?
4. What is the sum of \( P(E) \) and \( P(\text{not } E) \) when \( P(E) = 0.6 \)?
5. How do you calculate the probability of either event \( E \) or event \( F \) occurring?

**Tip:** The sum of the probabilities of an event and its complement is always 1. This can be a useful check to ensure your probability calculations are correct.

Explore the relationship between probabilities of an event and its complement. Learn how to solve the fill in the blanks problem involving probability. Suitable for students in Grades 9-12.

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