## STATS FOR DS

# Mutually Exclusive And Independent Events

Let’s consider a trial of flipping a coin. The sample space is S={‘Head’,’ Tail’}.

If we flip the coin once, it will be either Head or Tail, the occurrence of one event(H or T) stops or affects the occurrence of the other event, hence they are called mutually exclusive events.

The probability of mutually exclusive events in a trial can be represented mathematically as: P(H AND T)=0 OR P(H ∩ T)=0;

Since there will be no common element (intersection) in the outcomes of the trial, either H or T (not overlapping sets).

Now consider a trial of flipping two coins at once . The sample space is S ={ (H,T),(T,T),(T,H),(H,H) }.

The output could be anything from the S, therefore the occurrence of one event on one coin(let’s say H) does not affect or stops the occurrence of another element(T), which could appear on the other coin in a trial. Such events are known as Independent events.

The probability of independents events in a trial can be represented mathematically as: P(H AND T)=P(H)*P(T) OR P(H ∩ T)=P(H)*P(T)

Although the events occur simultaneously, there could be common elements (intersection) in the outcomes of the trial HH, TT (overlapping sets).

** P(H)=P(T)=1/2 in both trials.