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What is the probability of A or B if A and B are independent?
If A and B are independent, then the probability that events A and B both occur is: p(A and B) = p(A) x p(B). In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B.
Are the complements of independent events also independent?
In conclusion, if two events are independent, then their complements are also independent.
How do you prove sets are independent?
Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) = P(B ∩ A) = P(B) × P(A).
How do you prove you are independent?
Test for Independence To test whether two events A and B are independent, calculate P(A), P(B), and P(A ∩ B), and then check whether P(A ∩ B) equals P(A)P(B). If they are equal, A and B are independent; if not, they are dependent.
When do A, B, and C are independent events?
Of course, as noted by Deep North, if A, B, and C are mutually independent events (which requires not just independence of B and C but also for P (A\\cap B \\cap C) = P (A)P (B)P (C) to hold), then A and B\\cap C are indeed independent events. Mutual independence of A, B and C is a sufficient condition.
Which is the independent clause in a subordinating conjunction?
Subordinating conjunctions allow writers to construct complex sentences, which have an independent clause and a subordinate (or dependent) clause. Either clause can come first. The students acted differently whenever a substitute taught the class. Whenever a substitute taught the class, the students acted differently.
What happens if A, B, and C are mutually independent?
If A, B, C are mutually independent,the results are obvious. While the condition is A and B are independent and A and C are independent do not guarantee independent of B and C Therefore, the OP may need to reexamine the condition of the question.
What’s the difference between a dependent and independent clause?
Independent Clause. An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence. Jim studied in the Sweet Shop for his chemistry quiz. Dependent Clause. A dependent clause is a group of words that contains a subject and verb but does not express a complete thought.