Something to specify then for next time.
* all the girls in the country are called Mary. Half the boys are Peter, the other half Paul.
* Mary was a child selected by random of all the children of two-child families in the country to present a bouquet of flowers to the great leader.
* when the great leader received the bouquet, he wanted to ask about Mary's sibling. But he had forgotten the gender of the sibling from his briefing data, and wanted to look good.. so he chose to ask randomly. But it was nice to optimise odds so he asked, "How is your brother, little Mary?"
A variant of the same is a magician has three playing cards. One is white on both sides, one is white on one side and black on the other, one of black on both sides. he picks a card at random and sees that the visible side is white. The odds of the other also being white is..
a. 1/2 as there are two cards, white-black and white-white; or
b. 2/3 as there are three sides of cards, WHITE-white, white-WHITE, and white-black.
Yet another variant is the famous two-goats-and-a-car gameshow.
There are three curtains, A, B, and C. One has a car behind it, the other two have goats (or gift certificates to get a car or goat so the size of the curtain and animal smell and sounds are no hint). Contestant can pick what is behind a curtain of his choice. He chooses A, at which point the host removes a curtain.. say, curtain C.. and show that that one was a goat. The contestant can change his mind at this point and pick B instead of A. Is it beneficial for him to do so?