In a single throw of two dice.
Possible outcomes are as follow:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) ,
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) ,
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Total number of outcomes = 36
Favorable outcomes (i.e. not getting the same number) = All outcomes except (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
We know,
Probability of occurrence of an event = (Total number of favorable outcomes) / (Total number of outcomes)
Therefore, the probability of at least one boy in the family = 30/36 = 5/6