![]() Out of the 10 rolls, how often do you expect to get each number? After each roll, record which number you got in your tally sheet. What is the theoretical probability for each number? Write the probabilities in fraction form. ![]() Calculate the theoretical probability for rolling each number on a six-sided die.And after you multiply your numerator by 2, you will have a number that is out of 100-and a percentage.) Does your experimental probability match your theoretical probability from the first step? (An easy way to convert this fraction into a percentage is to multiply the denominator and the numerator each by 2, so 50 x 2 = 100. Again, write your results in fraction form (with the number of tosses as the denominator (50) and the result you are tallying as the numerator). Count how many heads and tails you got for your total coin tosses so far, which should be 50.How are they different from your previous results for the 10 coin tosses? Look at your results from the 30 coin tosses and convert them into fraction form.Record your results for each toss in your tally sheet. Compare your results from the second round with the ones from the first round.Do you expect the same results? Why or why not? So that would be 7 heads out of 10 tosses: 7/10 or 0.7. (The denominator will always be the number of times you toss the coin, and the numerator will be the outcome you are measuring, such as the number of times the coin lands on tails.) You could also express the same results looking at heads landings for the same 10 tosses. For example, 3 tails out of 10 tosses would be 3/10 or 0.3. Count how often you got heads and how often you got tails.After each toss, record if you got heads or tails in your tally sheet. ![]() Out of the 10 tosses, how often do you expect to get heads or tails? What is the theoretical probability for each side? Calculate the theoretical probability for a coin to land on heads or tails, respectively.Prepare a second tally sheet to count how often you have rolled each number with the die.Prepare a tally sheet to count how many times the coin has landed on heads or tails.So how do your theoretical probabilities match your experimental results? You will find out by tossing a coin and rolling a die in this activity. For example, outcomes with very low theoretical probabilities do actually occur in reality, although they are very unlikely. The interesting part about probabilities is that knowing the theoretical likelihood of a certain outcome doesn’t necessarily tell you anything about the experimental probabilities when you actually try it out (except when the probability is 0 or 1). In this activity, you will put your probability calculations to the test. Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent). In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). It gets more complicated with a six-sided die. This means that for the coin toss, the theoretical probability of either heads or tails is 0.5 (or 50 percent). The sum of all possible outcomes is always 1 (or 100 percent) because it is certain that one of the possible outcomes will happen. As long as the coin was not manipulated, the theoretical probabilities of both outcomes are the same–they are equally probable. If you toss a coin, there are two possible outcomes (heads or tails). If there is more than one possible outcome, however, this changes. If an event has only one possible outcome, the probability for this outcome is always 1 (or 100 percent). The probability of a certain event occurring depends on how many possible outcomes the event has. The higher the probability number or percentage of an event, the more likely is it that the event will occur. Probability can also be written as a percentage, which is a number from 0 to 100 percent. This means a probability number is always a number from 0 to 1. In mathematics, these extreme probabilities are expressed as 0 (impossible) and 1 (certain). You probably also know that the probability of an event happening spans from impossible, which means that this event will not happen under any circumstance, to certainty, which means that an event will happen without a doubt. You might be familiar with words we use to talk about probability, such as “certain,” “likely,” “unlikely,” “impossible,” and so on. Probability allows us to quantify the likelihood an event will occur. In this activity, you will do these calculations and then test them to see whether they hold true for reality! This means that for certain events you can actually calculate how likely it is that they will happen. Probability tells you how likely it is that an event will occur. Have you ever heard anyone say the chance of something happening is “50–50”? What does that actually mean? This phrase has something to do with probability.
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