![]() ![]() You can load most data sets into R with one simple step, see Loading Data. When you are finished, your deck of cards will look something like this: face suit valueĭo you need to build a data set from scratch to use it in R? Not at all. In short, you’ll build the equivalent of an Excel spreadsheet from scratch. You’ll start by building simple R objects that represent playing cards and then work your way up to a full-blown table of data. (See the tables below.In this chapter, you’ll use R to assemble a deck of 52 playing cards. A dice labelled 1, 2, 3, 9, 10, and 11 nearly works: it will beat red, has a small advantage over yellow, and is the equal of blue. In the long run, you would expect red to win 16 out of 36 times and yellow to win 20 out of 36 times.Ĥ. In the long run, you would expect blue to win 22 out of 36 times, yellow to win 12 out of 36 times, and a draw 2 times out of 36.Į. When it is blue versus red, you can expect that in the long run, red will win 22 out of 36 times, the two dice will draw 2 out of 36 times, and blue will win 12 out of 36 times.ĭ. Increasing the points should make no difference.ī. (See the results for question 3 below.) So no dice is the “best dice” in all circumstances. Results will vary, but in the long run, it should become clear that each dice can beat another one and can be beaten by another one. (You need to be aware that the higher numbers are more likely to score the points in this competition.)Ģ. A dice could be picked because it has high numbers or no low numbers. The tables in the Answers are the basis on which the theoretical probability of success for each dice is calculated. The sample space is the complete set of all possible outcomes. If the students have already met probabilities as fractions, they can make use of the following formula, which looks very similar to the one above but uses numbers that can be precisely determined (rather than obtained from trials): If a group of students is playing simultaneous games, recording the results on a master table will quickly give enough trials to provide a very accurate result for the experimental estimate of probability. After 50 trials, the students should have a tentative experimental estimate of the probability, and after 100 trials, they should have a result that is unlikely to change much with further trialling. But as the number of trials increases, a trend will emerge in which one colour is dominant. You will need to explain these words if the formula is to make sense to the students.Īt first, when the students play with the dodgy dice, one colour will win, then the other, with no discernible pattern. R DICE WITH 100 TRIALS TRIALA trial is an attempt to get the desired outcome. Note that an event is something you want to happen (like getting an odd number when throwing a dice or getting blue to win). This useful concept means that if you do not know the probability of something happening, you can work it out (experimentally) by completing a large number of trials and then You should also revise the language of probability.ĭodgy Dice is best used following Wallowing Whales (pages 20–21 of the students’ book), which introduces the idea of long-run relative frequency. If this is true of your students, you will need to work on these skills before assigning this activity. See Unfortunately, many students do not have these skills and are especially weak on fraction concepts. Entering the results into a table is a simple and logical development of these level 4 skills. In the exemplars, students not only use fractions to record probabilities but deal with more sophisticated investigations by systematically counting all outcomes or using tree diagrams and then assigning numerical probabilities ![]() This activity reflects level 4 of the mathematics exemplars rather than the curriculum document. ![]()
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