Independent and dependent Events

Two events are said to be independent if the result of the second event is not affected by the result of the first event.

If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events.

If A and B are independent events, P (A and B) = P (A) * P (B).

The probability of heads landing up when you flip a coin is 1/2.What is the probability of getting tails if you flip it again 1/2 It is still 1/2.The two events do not affect each other. They are independent.

If the result of one event is affected by the result of another event, the events are said to be dependent.

If A and B are dependent events, the probability of both events occurring is the product of the probability of the first event and the probability of the second event once the first event has occurred.

If A and B are dependent events and A occurs first,

P(A and B) = P(A) * P(B, once A has occurred) is written as ...

P (A and B) = P (A) * P (B/A)

There are 3 red pebbles left in a bag of multicolored pebbles with a total of 20 pebbles left in it. The probability that you will get a red one when you reach in is: 3/20.

But what are your chances of getting a red one if you reach in again?

There are now 19 pebbles in the bag, and only two are red.

The probability is 2/19.

Taking the first pebble affected the outcome of the next attempt.

The two events are dependent.

In case of three events

For three dependent events A, B, C, we have

P(A and B and C) = P(A) * P(B | A) * P(C | A and B)

For three independent events E1, E2, E3, we have

P(A and B and C) = P(A) * P(B) * P(C)