Category: probabilities

Last Problem:

Six men check their hats at the theater. An inattentive attendant mixes up the claim checks, so when the men return after the show the hats are essentially handed out at random.

If someone offered you even money to bet that at least one of the men got his own hat back, would you take the bet? In other words, do you believe that the probability of one of the six men getting his own hat back to be greater than .5?

Answer:

You should take the bet. The probability of at least one man getting his own hat back is almost .632.

Today’s Problem:

You participate in a virtual reality game in which you are given the chance to fight either one brontosaurus or three smaller stegosaurs in a row.

You know in advance that your chances of defeating the brontosaurus are one in seven, while the probability of defeating one of the stegosaurs is 1/2.

Which alternative should you choose? That is, which choice gives you the better chance of winning the game?

Last 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?

Answer:

The chances of drawing a red ball are 20/50 or 40%. The chances of drawing a blue ball are 30/50 or 60%.

Today’s Problem:

Six men check their hats at the theater. An inattentive attendant mixes up the claim checks, so when the men return after the show the hats are essentially handed out at random.

If someone offered you even money to bet that at least one of the men got his own hat back, would you take the bet? In other words, do you believe that the probability of one of the six men getting his own hat back to be greater than .5?

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?