False Positive HIV Test

Imagine an HIV test that is 95% accurate (false positive rate of 5%) and around 2% of the tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive?

29%

To read more about this, see the False Positive Paradox page on Wikipedia.

Posted in Brain Teasers

amid eerie nighed won spawn

What phrase do these words sound like when rearranged?

amid eerie nighed won spawn

“Won spawn amid nighed eerie” sounds like, “Once upon a midnight dreary”, from The Raven by Edgar Allan Poe.

Posted in Brain Teasers

Placed On the Table But Never Eaten

What is placed on the table, cut and passed but never eaten?

A deck of cards. You play card games on a table, cut the deck, then deal (or pass out) the cards, but you only eat the snacks.

Posted in Riddles

None There’ll Be

There is a word of letters three,
Add one letter to it and none there’ll be.

What is the word?

One. Add an ‘n’ to get none.

Posted in Riddles

Remove Four And I’m The Same

I am an English word with five letters. If you remove my last four I am still pronounced the same. What am I?

Queue.

Posted in Riddles

Only Hides in the Unwound

What can be seen but never found that only hides in the unwound?

Relaxation. You can see when someone is relaxing, but no one can remain completely relaxed forever. You can relax more easily as you learn to unwind.

Posted in Riddles

At Least One is a Boy

A couple has two children. At least one of them is a boy. Assuming the probability of having a boy or girl is 50%, what is the probability that both children are boys?

If you answered 1/2, you’re not without comrades, but the generally accepted answer by statisticians (though not without debate) is 1/3. This is because there are four possible combinations: boy-boy, boy-girl, girl-boy and girl-girl. Since we are told one of the children is a boy (but we don’t know if it’s the first or second child), we can rule out the girl-girl combination, leaving three remaining options. Only one out of 3 is boy-boy, so we get a 1/3 chance.

This is a well-known problem known as the Boy or Girl paradox. The other variation is this brain teaser.

Posted in Brain Teasers

Sum of 22

Fill in numbers such that the sum of each 3-character row is 22 while the sum of all five numbers is 30.

a
bcd
e

The problem works out to a set of three equations:
b + c + d = 22
a + c + e = 22
a + b + c + d + e = 30

Solving for c = 14, leaving d = 8 – b and e = 8 – a. In other words, c must be 14, but the other two numbers just have to add up to 8. The requirement that they be unique rules out 4 + 4, so you’re left to choose from the following combations for b + d and a + e:
0 + 8
1 + 7
2 + 6
3 + 5

Posted in Brain Teasers

I Can Be Long or Short

I can be long, or I can be short.
I can be grown, and I can be bought.
I can be painted, or left bare.
I can be round, or square.
What am I?

A fingernail.

Posted in Riddles

If I Can I Can

If I can, I can,
If I can’t, I freeze.

What am I?

Someone preserving food. The two most common ways of preserving food are canning and freezing. So when you preserve food, if you can can it, you do, otherwise you freeze it.

Posted in Riddles