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Probability of Two Independent Events

TopIf we have any two events, say A and B then the two events are said to be independent if the occurrence of first event A does not affect the Probability of the occurrence of the event B. If we consider the following pair of events one after another, we conclude that they are not affecting the probability of one another, so they are called probability of two Independent Events
Following examples show the probability of two independent events:
1. Choosing a marble from a pot AND throwing and rolling a number 4 on a single six sided dice.
2. Choosing a king from a pack of cards AND then landing a head on the tossing of a coin
3. Rolling 3 on a dice AND then rolling 1 on the second roll of a dice.
4. Choosing J from the pack of cards, AND then replacing it back and taking out K from the pack of the card.

Let us try an experiment of taking out a pair of socks from a drawer, which has five pairs of socks in it. The colors of the socks are red, blue, white, pink and black. If a child takes out a pair of socks from a drawer without seeing at it, again the socks taken out from the drawer is replaced back to make the number of socks exactly 5 and then another attempt is taken to take out a pair of socks again. Now if we find the probability of getting black socks in the first attempt AND Red socks in second attempt, we observe that the second event is not affected by the first one as before the second event, a pair of socks is replaced back. Such an events are called compound events. Since the two events are independent
The probability of two independent events can be shown by:

P (A AND B) = P(A) . P(B)
In such cases we find the probability of two events independently and then find their product.
Here P(A ) = 1/5 and P(B) = 1/5,
So P(A AND B )= (1/5) . (1//5) = 1/25.