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How often will a die come up "4"? How likely is it to rain tomorrow? Probability is one of the most powerful frameworks for modeling the world around us.

Ari has a box of tulip bulbs. Of the bulbs in the box, 6 will grow into red tulips, 3 will be white tulips, 4 will become yellow tulips, and 7 will bloom into blue tulips. Ari does not have any bulbs for other colors of tulip.

If Ari selects a bulb at random, what are the chances it will grow into a red tulip?

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Justin has two fair six-sided dice. Each die is numbered with the integers from 1 to 6.

Justin claims that if he rolls both dice, their sum can have any integer value between 2 and 12 inclusive, which represents 11 distinct possibilities. Therefore, the chance that he will roll a sum of 12 is \(\frac{1}{11}\).

Is Justin's statement true or false?

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Two players are playing a game. They roll a fair 10-sided die, where each face has a different integer from 1 to 10.

If the die roll is 6 or greater, Player A gets a point. If it’s an even number, Player B gets a point.

For any given die roll, what is the probability that B gets a point, but not A?

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A math student is attending a class that meets every weekday (Monday through Friday), but not on weekends.

On Monday, April 1, the student’s teacher announces that she has randomly selected 4 classes in April to have pop quizzes.

By Sunday, April 14, the class has only had 1 pop quiz. What is the probability that the following day (Monday April 15) will have a pop quiz?

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A teacher is giving his class a 10-question quiz. However, in order to prevent cheating, each copy of the quiz has the 10 questions in a random order.

What is the probability that two students who are sitting next to one another will have the same version of "Question 1" on both quizzes?

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