Suppose that we toss two fair coins simultaneously in a room, then intuitively the outcome of one coin does not affect in any way the outcome of other coin. This concept is known as Independence. The events A and B are independent only and only if

\(P(A \cap B) = P(A) \times P(B)\)

Where \(P(A \cap B)\)is the probability of occurrence of event \(A\) and \(B\) together

Also note the following notations.

\(P(A \cup B)\)= Probability of occurrence of at least one event of A and  B.

\(P(A \cap B)\)= Probability of occurrence of event A and B together

\(P(\bar A \cap B)\) = Probability of occurrence of event B only.

\(P(A \cap \bar B)\)= Probability of occurrence of event A only.

Questions 01: Three dice are thrown randomly, find the probability that at least one of them is showing 3.