It's a paradox only because how question is put. Your wife says that neighbours have children, and she observed a boy. Then she observed boy again. What difference in probability having neighbours having a girl if you seen a boy once or twice.

You have red and black pebbles otherwise identical. Bag has 2 pebbles, you draw a pebble, it's red. You put it back. What's the probability of bag having black and red pebble? Draw again - red again. What's the probability of bag having black and red pebble? You acquire more data, therefore your estimate changes.