Tree Diagram

Probability of event to happen P(E) = Number of favourable outcomes / Total Number of outcomes

Assume an event E can occur in r ways out of a sum of n probable or possible equally likely ways. Then the probability of happening of the event or its success is expressed as- P(E) = r/n

The probability that the event will not occur or known as its failure is expressed as- P(E’) = (n-r)/n = 1-(r/n)

E’ represents that the event will not occur. Therefore, now we can say that - P(E) + P(E’) = 1

For example, when we toss a coin, either we get Head or Tail, only two possible outcomes are S= {(H,T)}.

E=event of occurrence of Head E’=event of not occurrence of Head or the occurrence of Tail

Then P(E) =P(H) = 1/2 =0.5;
P(E’) = P(T) = 1/2 =0.5