Consider four independent trials in which an event A occurs with probability $\frac{1}{3}$ in any single trial. The event B occurs with probability 1 if the event A occurs atleast twice, it can not occurs if the event A does not occur and it occurs with probability $\frac{1}{2}$ if the event A occurs only once. If the probability p of the occurrence of event ‘B’ can be expressed as $\frac{\mathrm{m}}{\mathrm{n}}$ , then the least value of (m + n), where $\mathrm{m},\mathrm{n}\in \mathrm{N}$, is