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# Probability of Dependent and Independent Events

TopIndependent events and dependent events both work on same formula, but there is a lot of difference between them Independent Events are those events while occurring of one event there is no relation with the second event but in dependent event if we are having two events, let’s say ‘A’ and ‘B’ and there will be a relation between ‘A’ and ‘B’ and there will be a change in the probability of the combined due to dependency. If we draw a card from a deck of 52 cards and without replacing it we draw another card this is the example of Dependent event and in the above example we draw the card without replacing then that will be an independent event. Both independent event and dependent events can be well understood with the help of an example given below,
Example 1: If a card is chosen from a stranded deck of 52 cards. Without replacing it, another card is chosen. Now you need to find the probability that the card is a king and then a ace?
Solution: As we are seeing both the events are related to each other so it is a dependent event so we can solve it by the multiplication formula that is given below,
P (A and B) = P(A) · P(B),
Here p (A) and p (B) is the probability of two events ‘A’ and ‘B’, and P(A and B) is the combined probability of both,
Probability of getting a king= 4/52 = 1/13,
probability of getting a king= 4/51( as we chosen a card without replacing that means we are having 51 card as a king is already drawn).
P (A and B) = 1/13*4/51,
P (A and B) =4/663,
And if the events are independent then probability will be,
P (A and B) = 4/52* 4/52,
P (A and B) = 1/169,
In this way we can Calculate The Probability of dependent and independent events.