The conclusion that can be drawn from the given statements is that " events E and F are independent".
When are independent events?
Two events such as A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B. I.e.,
P(A ∩ B) = P(A)×P(B)
What is conditional probability?
If A and B are two events in a sample space S, then the probability of event B after event A has occurred is called the conditional probability and it is denoted by P(B|A) = [P(A ∩ B)]/P(A).
Verifying how the given events are related:
Given that E and F are two events.
P(E|F) = 0.3
P(E) = 0.3
So, the conditional probability is written as,
P(E|F) = P(E ∩ F)/P(F)
If E and F are independent events, then the probability P(E ∩ F) = P(E) × P(F).
On substituting,
P(E|F) = P(E) × P(F)/P(F)
= P(E)
Therefore, P(E|F) = P(E) = 0.3
Hence, events E and F are independent.
Learn more about independent events here:
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