Which is a pair of independent events?

Definition of Independent Events

In probability, two events are independent if the outcome of one event does not influence the outcome of the second event. A good example of a pair of independent events is when we roll a die and then flip a coin. The number showing on the die has no effect on the coin that was tossed.

What type of events are A and B if P A ∩ B )= 0?

Mutually exclusive events cannot occur simultaneously. Formally said, the intersection of each two of them is empty (the null event): A∩B= ϕ. In consequence, mutually exclusive events have the property: P(A∩B)=0.

What is the formula for mutually exclusive events?

If A and B are said to be mutually exclusive events then the probability of an event A occurring or the probability of event B occurring that is P (a ∪ b) formula is given by P(A) + P(B), i.e., P (A Or B) = P(A) + P(B)

How do you find the probability of the union of two independent events?

The general probability addition rule for the union of two events states that P(A∪B)=P(A)+P(B)−P(A∩B) P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) , where A∩B A ∩ B is the intersection of the two sets. The addition rule can be shortened if the sets are disjoint: P(A∪B)=P(A)+P(B) P ( A ∪ B ) = P ( A ) + P ( B ) .

What is nCr formula?

Combination: nCr represents the selection of objects from a group of objects where order of objects does not matter. nCr = n!/[r! (n-r)!] Where n is the total number of objects and r is the number of selected objects.

What is the formula for independent events?

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

For which of the following probability assignments are events A and BB independent?

Two events A and B are said to be independent if and only if P(A / B) = P(B) or P(B / A) = P(A). If P(A) > 0, P(B) > 0, and P(A nB) = 0, then the events A and B are independent.

What is dependent and independent event?

An independent event is an event in which the outcome isn’t affected by another event. A dependent event is affected by the outcome of a second event.

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