In total, we have 2 + 3 = 5 persons.


Of 5 persons, we can form   = 5*2 = 10 different pairs, in all.


It is our full space of events in this problem.



    From the other hand side, we can select one man of two men by 2 ways;

    and we can select one woman of three women by 3 ways;

    so we can select a pair (man,woman) by 2*3 = 6 way: there are 6 different pairs of this kind.



So, among total possible 10 pairs of the space of events, we have 6 possible different pairs (man,woman).


This set of 6 such pairs is the space of the favorable events.


Now the probability under the problem's question is


    P =  =  = 0.6 = 60%.      ANSWER