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You have two events A and B such that [tex]P(A|B) = 0.4[/tex] and [tex]P(A) = 0.4[/tex]. Based on this information, what can you conclude?

A. Event A is not dependent on Event B.
B. Event A is dependent on Event B.
C. Event B is dependent on Event A.
D. Events A and B are dependent on each other.
E. It is not possible to determine if the events are independent.

Sagot :

GinnyAnsweridn
To determine the relationship between events A and B, let's analyze the given probabilities:

1. Given Information:
- [tex]\( P(A|B) = 0.4 \)[/tex]
- [tex]\( P(A) = 0.4 \)[/tex]

2. Understanding Conditional Probability:
- [tex]\( P(A|B) \)[/tex] represents the probability of event A occurring given that event B has occurred.
- [tex]\( P(A) \)[/tex] represents the probability of event A occurring without any condition on event B.

3. Independence of Events:
- Two events A and B are considered independent if the occurrence of one event does not affect the probability of the occurrence of the other event.
- Mathematically, events A and B are independent if [tex]\( P(A|B) = P(A) \)[/tex].

4. Comparison:
- Here, [tex]\( P(A|B) = 0.4 \)[/tex] and [tex]\( P(A) = 0.4 \)[/tex].

Since [tex]\( P(A|B) = P(A) \)[/tex], it indicates that the occurrence of event B does not affect the probability of event A.

Conclusion:
- Option A is correct: Event A is not dependent on Event B.
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