I Challenge My Mind Every Day

Last Problem:

You begin a game with four cards. Two have a red pattern and two have a blue pattern and all are blank on one side.

You shuffle the four cards and place them face down. If you pick two cards at random, what is the probability that the two card will be the same color?

Your friend tries to convince you that the chances are 2/3 with this reasoning: There are three possibilities – two red, two blue or one of each – and since two of those are of the same color, the chances are two out of three. Are you convinced or not?

Answer:

The chances are not 2/3 but 1/3. The reasoning is simple. Choose any card. Of the three remaining cards, there can be only one that is the same color. The chances that you will pick it are only one in three.

Your friend has the problem figured incorrectly. The three possibilities he has identified are not equally as likely to happen.

Today’s Problem:

How many different outcomes are possible in the toss of two coins? [Perhaps this is not so obvious as it might seem at first glance?]

Last Problem:

Which of the following statements is true”

1) One statement here is false.

2) Two statements here are false.

3) Three statements here are false.

Answer:

Only the second statement is true. Statement number 3 rules out both statement number 1 and statement number 3.

Today’s Problem:

You begin a game with four cards. Two have a red pattern and two have a blue pattern and all are blank on one side.

You shuffle the four cards and place them face down. If you pick two cards at random, what is the probability that the two card will be the same color?

Your friend tries to convince you that the chances are 2/3 with this reasoning: There are three possibilities – two red, two blue or one of each – and since two of those are of the same color, the chances are two out of three. Are you convinced or not?