Most of the conceptual tasks in probability for these kind of events can be handled with the binomial distribution. The throw of a die or the picking of a card out of a deck are perhaps the most visible examples of the statistics of random events.
So the probability of a 7 on the dice is 1/6 because it can be produced in 6 ways out of a total of 36 possible outcomes. The probability of getting a given value for the total on the dice may be calculated by taking the total number of ways that value can be produced and dividing it by the total number of distinguishable outcomes. For example, throwing a 3 is twice as likely as throwing a 2 because there are two distinguishable ways to get a 3. This simple example raises the idea of distinguishable states. There are six ways to get a total of 7, but only one way to get 2, so the "odds" of getting a 7 are six times those for getting "snake eyes". But in the throw of two dice, the different possibilities for the total of the two dice are not equally probable because there are more ways to get some numbers than others. For the throw of a single die, all outcomes are equally probable. The probababilities of different numbers obtained by the throw of two dice offer a good introduction to the ideas of probability. How did we simulate the dice roll? The RANDBET function allowed us to do just that! Once we set up the function for 1 pair of dice, we easily copied and pasted it 499 more times to simulate 500 times.Statistics of Dice Throw Statistics of Dice Throw We simulate random dice rolls 500 times and then make a note in the third column every time a pair of the same numbers is achieved! In the blue table to the right, we notice that indeed the observed probability is very close to our calculated probability of 1/6. In our spreadsheet below, we have two dice (an orange and a black one). So, the probability of rolling any pair can be computed as the sum of 1/36 + 1/36 + 1/36 + 1/36 +1/36 + 1/36 = 6/36 = 1/6.ĭoes this really hold true? If we rolled the dice a very large number of time, can we expect this outcome would occur 1/6 time in the long run? Let’s use spreadsheets to find out! This probability of both dice rolling a 2 or 3 or 4 or 5 or 6 is also 1/36. As such, the probability of both dice (dice 1 and Dice 2) rolling a 1 is 1/36, calculated as 1/6 x 1/6. The probability of Dice 2 rolling a 1 is also 1/6. The probability of Dice 1 rolling a 1 is 1/6. As such, the probability of rolling a pair of the same numbers is 6 x 1/36 or 6/36, which is equal to 1/6.Īnother way to think about this is as follows. As shown above, we highlighted all those outcomes that are pairs, which occur 6 times. Each outcome is equally likely, so the probability of each is 1/36. The sample space consists of 36 outcomes. When we consider the sample space for a pair of dice, the sample space expands by six-fold. In the case of a throw of a single dice, the sample space is as follows: 1, 2, 3, 4, 5, and 6. The sample space of a random coin toss is Heads and Tails. This collection of all these outcomes is also known as the sample space.įor instance, let’s consider the chance event of tossing a coin. When approached with a question about probability, a good first step is to consider all possible results of observing the outcomes of a chance event. We use the laws of probability to understand the chances of successful outcomes in our uncertain world. What is the probability of rolling any pair of numbers with two dice? Let’s first solve this and then confirm our calculated probability by simulating 500 dice rolls with a spreadsheet! In this post, we will focus on understanding basic probability concepts and then discover how with spreadsheets, we can actually see whether our calculated probability holds true!
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