Two Coin Toss

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?]

The Card Game: What is the Probability that …

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?

Which of These Three Statements is True?

Yesterday’s Problem:

A teacher held up a piece of paper and asked his students to tell him how many squares they saw. His students replied:

Six, they replied.

Which was the correct answer.

The teacher then held up the paper again and asked his students how many squares they saw.

“Eight,” they replied, again correct.

How can this be? How many squares were really on the sheet? Six? Eight? Or?

Answer:

There were fourteen squares on the sheet – six on one side and eight on the other side.

Today’s 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.

How Many Squares Are There?

Last Problem

There is a secret word hidden in the following matrix of letters. Can you discover it? Can you unlock the code?

R V E O V C
S I O V R D
V E R C V O
R O V E S E
E R S C R I
C E R E O R

Answer:

If you count the letters, you will find there is 1 D, 2 I’s, 3 S’s, 4 C’s, 5 O’s, 6 V’s, 7 E’s and 8 R’s. The secret word is thus DISCOVER which is what you were ask to do in the problem. “Can you discover it?”

Today’s Problem:

A teacher held up a piece of paper and asked his students to tell him how many squares they saw. His students replied:

Six, they replied.

Which was the correct answer.

The teacher then held up the paper again and asked his students how many squares they saw.

“Eight,” they replied, again correct.

How can this be? How many squares were really on the sheet? Six? Eight? Or?