Last Problem:
Three children make the following statements:
Child #1 [Frank]:
I am a truth teller.
Child #2:
Frank says he is a truth teller.
Child #3:
Frank is not a truth teller – he is a liar.
The three children quoted above are either truth tellers or liars. Can you tell with certainty how many of each there are?
Answer:
Child #1 [Frank] says he is a truth teller. The statement is true if he is telling the truth and false if he is lying.
What Child #2 says is true no matter whether the first child is telling the telling the truth or lying. Child #2 is therefore a truth teller.
The truth of Child #3 depends on the truthfulness of the first child (Frank). If the first child is lying, the third child is telling the truth. If the first child (Frank) is telling the truth, the third child is lying.
The possibilities are either [liar-truth teller – truth teller] or [truth teller – truth teller – liar]. Either way, two are telling the truth and one is lying. The question does not ask which child is telling the truth and which one is lying.
Today’s Problem:
A container holds 20 red balls and 30 blue balls. If you draw a ball out of the container without looking, what is the probability that it will be a red ball?