By Girardi M., Mataloni S., Matzeu M.

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**Extra resources for Existence of classical solutions for fully non-linear elliptic equations via mountain-pass techniques**

**Example text**

A has a bigger chance of winning. You may need to play the game to find this out. ” You can find the chance for rolling a double with two number cubes from the chart in Section A. So the chance of doubles is less than the chance of “not doubles,” which means that A (who wins if no double occurs) has a bigger chance of winning. 2 a. If you roll a number cube a thousand times, you would expect 1 of the rolls, so about 1000 —— = 167 times. a 6 to come up in about ᎑᎑ 6 6 b. The numbers divisible by three on a number cube are 3 and 6, which is one third of the numbers on the number cube.

These are the results: Number of Questions out of Five Correct Number of Times This Occurred 0 9 1 16 2 13 3 5 4 7 5 0 c. Based on these results, what is the chance that Peter will get three or more questions on the quiz correct by guessing? Think of a situation different from the ones in this section where you would have to simulate the situation many times to estimate the chance of an outcome. Think of another situation where you could figure out the theoretical chance and would not need to simulate the situation.

Write the chance as a fraction and as a percent. b. What is the chance, as a percentage, of rolling “not 1s” with six number cubes in the game of Hog? 2. Mr. and Mrs. Lewis have four daughters. You may assume that the chance of having a son is the same as having a daughter: 1᎑᎑2 . Comment on each of the following statements. a. The chance that their next child is a girl is smaller than 1᎑᎑2 because a family with five daughters is very unlikely. b. The chance is one half because the chance of a girl is 1᎑᎑2 .