Description
1. Let X be the random variable that is defined as the greater of the two numbers that appear when a pair of dice is rolled. For example, if you roll 2 and 5, then X = 5.
2. Botanists at UMass Boston recently discovered a new local flower species that they named the Boston powerflower. It has beautiful, blue blossoms, and each flower lives for only one summer. During that time, each flower produces 13 seeds. Three of these seeds will turn into flowers in the following year, and the remaining ten seeds will turn into flowers the year after. As the name powerflower suggests, these seeds always turn into flowers; there is no failure ever. During the year of this discovery (let us call it year zero), the scientists found three powerflowers on the UMass campus, and in the following year (year one), there were already eight of them.
3. Let us assume that the probability of the Boston Red Sox to beat the New York Yankees at a baseball game is 70% and that no ties are possible, i.e., the New York Yankees win 30% of the time. Furthermore, the result of each game is independent of the results of any previous games.
4. Urns and Probabilities