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## Which equation implies that A and B are independent events?

If A and B are independent events, that means the likelihood of one event happening is independent of the other event happening. The outcomes do not depend on each other and are unaffected by the other outcome.

For example:

A = rolling a die and getting a 2

B = flipping a coin and getting heads

These events are independent because whatever you roll on the die doesn’t affect what might happen with the coin toss.

With independent events, the probability of both events happening is simply the product.

P(A and B) = P(A) x P(B)

P(A) = 1/6 <– rolling a 2

P(B) = 1/2 <– flipping heads

P(A and B) = 1/6 x 1/2 = 1/12 <– rolling a 2 and flipping heads

Answer:

#4

What is the probability of event A if A and B are – It is given that both the events A and B are independent with their respective probabilities P (A)=0.6 and P (B)=0.4. As they are independent, product of their probabilities is the probability of occurring of both events simultaneously i.e. P (A and B)=P (A)*P (B) So we have P (A and B)= 0.6*0.4=0.24 According to the addition law of probabilityExample . A box contains two coins: a regular coin and one fake two-headed coin ($P(H)=1$). I choose a coin at random and toss it twice. Define the following events.If A and B are independent events, then the probability of A happening AND the probability of B happening is P (A) × P (B). The following gives the multiplication rule to find the probability of independent events occurring together.

Conditional Independence – Course – Two events A and B are independent iff P (A∩B) = P (A)P (B). This definition extends to the notion of independence of a finite number of events. Let K be a finite set of indices. Events A k, k∈K are said to be mutually (or jointly) independent iffStack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange1 The definition of " {A,B,C} is independent" implies that the equation you wrote is true, as well the pairwise equations being true.

Independent Events (solutions, examples, videos) – gradient23's proof is great, in my opinion, but I would like to show another proof that seems more intuitive to me, though much less rigorous.. The proof is based on a verbal definition of independence from wikipedia:. two events are independent […] if the occurrence of one does not affect the probability of occurrence of the otherThe probability formula P(A and B) = P(A)*P(B) is used only for events that are independent. If this formula is used on events that are dependent, the result will not actually be the theoreticalIf events are independent, then the probability of them both occurring is the product of the probabilities of each occurring. Specific Multiplication Rule. Only valid for independent events P(A and B) = P(A) * P(B) Example 3: P(A) = 0.20, P(B) = 0.70, A and B are independent.