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This Exploration focuses on applying probability to games of chance. However, all of the techniques and mathematical tools we'll introduce can also be applied to many situations outside of games such as:

**Your Daily Life**

Guiding your daily choices and giving you intuition for what will result.**Politics and Debate**

Understanding how statistics can be misused in debates.**Science and Health**

Statistical intuition that is fundamental to the development of science and medicine.**Engineering and Product Design**

Creating safe, reliable products and technology.

And these are just to list a few!

**Probability problems appear everywhere and every day, yet the next 5 problems in this quiz are practical cases that trick even experienced problem-solvers!**

**Probability in Your Daily Life**

One day, the traffic light at a certain intersection is red when you reach it and no other cars are in front of you. You wait 45 seconds for it to turn green.

The next day you reach the same light and it's red again. Additionally, another car is already there, waiting for the light to change, and you pull to a stop behind him.

**How long should you expect to wait for the green light this time?**

NOTE: You may assume the light changes at regular intervals and does the time does not change when cars or near or based on the time of day.

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**Probability in Your Daily Life**

Suppose you have a bag with 5 chocolate caramels and 5 cherry cordials. Your friend grabs a candy at random and eats it. Afterwards, without looking at what's left, you grab and eat one of the remaining 9 candies. **What is the probability you just ate a cherry cordial?**

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**Probability in Politics and Debate**

The world's oldest Olympic medalist was 72 years old (Oscar Swahn of Sweden). Pictured above is Amy. **Which of these statements about her is more likely to be true?**

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**Probability in Science and Health**

For this puzzle, test your rapid-fire intuition by guessing without calculating, or do the calculation if you want.

Disease Z infects 1 out of every 1000 people. There's a test for Disease Z which is guaranteed to test positive for someone with the disease. For those without the disease, they will test positive 1% of the time.

You tested positive for Disease Z, and your doctor wants to place you on an expensive emergency treatment. **What's the probability you actually have it?**

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**Probability in Engineering and Product Design**

The matchsticks above represent fences protecting a sheep from a wolf. Observe that if two of the matchsticks are removed at random, then the wolf *might* be able to get to the sheep.

Now, would moving two matchsticks from the outer ring to the inner ring, as shown in the diagram below, make the sheep any safer when two matchsticks are removed at random?

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