Choose the three formulas that can be used to describe complementary events. 
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Part 1
Select the three formulas that can be used to describe complementary events.
A.StartFraction Upper P left parenthesis Upper E right parenthesis Over Upper P left parenthesis E' right parenthesis EndFraction equals 1
StartFraction Upper P left parenthesis Upper E right parenthesis Over Upper P left parenthesis E' right parenthesis EndFraction equals 1
B.
​P(E)plus​P(E')equals1
C.Upper P left parenthesis Upper E right parenthesis equals StartFraction 1 Over Upper P left parenthesis E' right parenthesis EndFraction
Upper P left parenthesis Upper E right parenthesis equals StartFraction 1 Over Upper P left parenthesis E' right parenthesis EndFraction
D.
​P(E)minus​P(E')equals1
E.
​P(E')equals1minus​P(E)
F.
​P(E)equals1minus​P(E')
G.Upper P left parenthesis E' right parenthesis equals StartFraction 1 Over Upper P left parenthesis Upper E right parenthesis EndFraction
Upper P left parenthesis E' right parenthesis equals StartFraction 1 Over Upper P left parenthesis Upper E right parenthesis EndFraction


Complementary events are two mutually exclusive events whose probabilities add up to 1. Let’s review the formulas given and determine which correctly describe complementary events:

1. **Formula A**: \(\frac{P(E)}{P(E')} = 1\)  
   This formula states that the ratio of the probabilities of \(E\) and its complement \(E'\) is 1, which is incorrect because \(P(E) + P(E') = 1\) is the key property of complementary events, not their ratio equaling 1.

2. **Formula B**: \(P(E) + P(E') = 1\)  
   This is a correct formula because it directly states that the probability of an event and its complement sums to 1.

3. **Formula C**: \(P(E) = \frac{1}{P(E')}\)  
   This formula is incorrect because it implies the probabilities of complementary events are reciprocals, which is not true.

4. **Formula D**: \(P(E) - P(E') = 1\)  
   This formula is incorrect because complementary events do not subtract to 1; their sum is 1.

5. **Formula E**: \(P(E') = 1 - P(E)\)  
   This is a correct formula, as it expresses the probability of the complement of \(E\) as 1 minus the probability of \(E\).

6. **Formula F**: \(P(E) = 1 - P(E')\)  
   This is correct since it expresses the probability of \(E\) as 1 minus the probability of its complement \(E'\).

7. **Formula G**: \(P(E') = \frac{1}{P(E)}\)  
   This formula is incorrect because it suggests that the probabilities of complementary events are reciprocals, which is not true.

**Correct Formulas:**
- **B: \(P(E) + P(E') = 1\)**
- **E: \(P(E') = 1 - P(E)\)**
- **F: \(P(E) = 1 - P(E')\)**

These formulas correctly describe complementary events.

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Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is the probability of the complement of an event with \(P(E) = 0.7\)?
2. How can you determine if two events are complementary?
3. What is the probability of an event if the probability of its complement is \(0.25\)?
4. How would you calculate the probability of either an event or its complement occurring?
5. What happens to the probability of an event if the probability of its complement increases?

**Tip:** Complementary events always cover all possible outcomes together, making their probabilities add up to 1.

Choose the three formulas that can be used to describe complementary events. Select the three formulas that can be used to describe complementary events. A. P(E) / P(E') = 1 B. P(E) + P(E') = 1 C. P(E) = 1 / P(E') D. P(E) - P(E') = 1 E. P(E') = 1 - P(E) F. P(E) = 1 - P(E') G. P(E') = 1 / P(E)

Learn how to identify and use the correct formulas for complementary events in probability. This problem covers essential probability concepts and is suitable for students in Grades 8-10. The solution explains why P(E) + P(E') = 1, P(E') = 1 - P(E), and P(E) = 1 - P(E') are the valid formulas for complementary events.

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