Let E and F be two events associated with a sample space S, then the set E ∩ F denotes the happening of two events E and F.
Example:
In the test of drawing second card after one, we can find probability of compound events a king and a queen. To find probability of event EF use conditional probability which is denoted by P(E/F) and is written as :
or P(E ∩ F) = P(F) - P(E/F) ...(i)
Similarly if event E is given then probability of F with condition is expressed as P \((\frac{F}{E})\) and can be written as:
P \((\frac{F}{E}) = \frac{P(E\ \cap \ F)}{P(E)}\)
Joining two conditions (i) and (ii)
P(E ∩ F) = P(F).P \((\frac{F}{E})\) = P(E).P \((\frac{F}{E})\)
whereas P(E) ≠ 0 and P(F) ≠ 0
Above result is known as multiplication law of probability.
