Category: probabilities

Last Problem:

How strongly do words affect perception? Practice reading the four lines of colored words below – but instead of saying the words, say the color of each word.

Can you say more than five words in a row without making a mistake? Or three?

Answer:

Well – of course there is no answer to this puzzle today. Why not give the challenge another trial run?

RED YELLOW BLUE GREEN

YELLOW BLUE GREEN RED

GREEN RED YELLOW BLUE

BLUE GREEN RED YELLOW

Today’s Problem:

Imagine if you will that you have been selected to be a guest on a game show that offers the chance to win a vacation on a Parkinsons Recovery Cruise. The prize sits behind one of the three doors: Monkeys (not real ones of  course) reside behind the other two doors.

You choose a door after much consternation. The host then opens one of the remaining two doors, revealing a monkey. The host then offers you a choice:

Stick with your initial choice or switch to the other door – still unopened of course.

What do you choose here? Stick with the door you initially chose or take the host up on the offer to peek inside the other door? The choice is important after all, since you will get to join others on a Parkinsons Recovery Cruise for free.

This puzzle should keep your neural networks firing for a few days!

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?