### Brain Teasers

# Itchy and Scratchy

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Itchy and Scratchy are playing Backgammon, which requires two identical dice to be rolled on each turn. Scratchy rolls the dice but just as they come to a halt on the board he covers them up with his hands.

"You can't look," screams Scratchy.

"Too late," yells Itchy. "I saw one of them and it was six! Show me the other one." Scratchy at first declines the offer but Itchy applies a gratuitous amount of violence with a chainsaw resulting in the amputation of both of Scratchy's arms, revealing the dice. If the first die revealed is a six, what is the probability that the second die is also a six?

"You can't look," screams Scratchy.

"Too late," yells Itchy. "I saw one of them and it was six! Show me the other one." Scratchy at first declines the offer but Itchy applies a gratuitous amount of violence with a chainsaw resulting in the amputation of both of Scratchy's arms, revealing the dice. If the first die revealed is a six, what is the probability that the second die is also a six?

### Hint

The answer is not 1/6.### Answer

Since Itchy saw one of the dice, the other one is either a six (1/6 chance) or a non-six (5/6 chance.)This means that if the scenario is repeated several times over, you would expect that on 5 out of every six occasions there would be one six and one non-six on the board in which case the hidden die is not a six. On the sixth occasion there are 2 sixes on the board so that either one may be revealed and still leave one six hidden. That means that out of every 7 occasions where a six can be revealed, 2 will result in a six remaining hidden.

Answer: Probability = 2/7

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