The probability of a certain event occurring depends on how many possible outcomes the event has. If an event has only one possible outcome, the probability for this outcome is always 1 or percent.
If there is more than one possible outcome, however, this changes. A simple example is the coin toss. If you toss a coin, there are two possible outcomes heads or tails. As long as the coin was not manipulated, the theoretical probabilities of both outcomes are the same—they are equally probable.
The sum of all possible outcomes is always 1 or percent because it is certain that one of the possible outcomes will happen. This means that for the coin toss, the theoretical probability of either heads or tails is 0.
It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes 1, 2, 3, 4, 5 or 6. Can you figure out what the theoretical probability for each number is? In this activity, you will put your probability calculations to the test.
For example, outcomes with very low theoretical probabilities do actually occur in reality, although they are very unlikely. 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. Observations and Results Calculating the probabilities for tossing a coin is fairly straightforward.
A coin toss has only two possible outcomes: heads or tails. Both outcomes are equally likely. This means that the theoretical probability to get either heads or tails is 0. The probabilities of all possible outcomes should add up to 1 or percent , which it does. When you tossed the coin 10 times, however, you most likely did not get five heads and five tails. In reality, your results might have been 4 heads and 6 tails or another nonand-5 result.
These numbers would be your experimental probabilities. In this example, they are 4 out of 10 0. When you repeated the 10 coin tosses, you probably ended up with a different result in the second round.
The same was probably true for the 30 coin tosses. Even when you added up all 50 coin tosses, you most likely did not end up in a perfectly even probability for heads and tails.
You likely observed a similar phenomenon when rolling the dice. Instead of rolling each number 17 percent out of your total rolls, you might have rolled them more or less often. If you continued tossing the coin or rolling the dice, you probably have observed that the more trials coin tosses or dice rolls you did, the closer the experimental probability was to the theoretical probability.
Overall these results mean that even if you know the theoretical probabilities for each possible outcome, you can never know what the actual experimental probabilities will be if there is more than one outcome for an event. This activity brought to you in partnership with Science Buddies. Already a subscriber?
Sign in. Thanks for reading Scientific American. Create your free account or Sign in to continue. For the first two dice, you need to throw either 1, 2, or 3 for both dice. The favourable outcomes are:. In other words there are nine favourable outcomes with two dice. Now each one of these has three possible favourable outcomes from the third dice ie.
The above rules apply when the items are independent , for example, dice or coins, and the outcome of the first one does not affect the second or subsequent events. However, it gets more complicated when the first event affects the second and subsequent events, that is, they are dependent. Dependent events are not as unusual as you might think. Consider drawing cards from a pack. If you do not replace the cards after each draw, you have a different number of possible outcomes each time.
In this case, you need to work out the probability of each event happening and then combine them in some way. The way that you combine them depends on whether you want to know the probability of either event, or both events OR or AND :. What is the probability of drawing at least one ace from a pack of cards on two draws, if you do not replace the cards in between?
Once you have drawn one ace, there are only 51 cards left from which to draw the second card, and only three of them are aces.
You want both events, so you need to multiply them. But now you have 51 cards left, all but three of which are not aces. The probability of drawing at least one ace when you draw two cards is therefore the probability of each of the three scenarios added together because you need only one to happen: they are OR events.
If you have trouble remembering whether you have to add or multiply for AND or OR, here are two easy ways to remember:.
The probability of throwing either a head or a tail from one coin is 1 it is a certainty. If your answer is greater than 1, you have probably added instead of multiplying. Many are listed as being for grades , but they would be relevant for an introductory level geoscience course.
Look in Exploring Data for finding and displaying data sets. Material on this page is offered under a Creative Commons license unless otherwise noted below. Show terms of use for text on this page ». Show terms of use for media on this page ». Your Account. Geologic context: forecasting, hazard assessment, error analysis, recurrence interval , radioactive decay.
Rolling dice, an excellent model of probability. There are a number of geologic contexts in which to introduce and explore probability. Molten lava flowing into the ocean. The U. S weather service defines several verbal probabilities:. One common source of confusion is that probabilities are represented in many differing ways all of which mean the same thing.
Show examples. Some ways of representing the same probability ratio - written as or 1 in 3. Tables are often used to show probabilities across a sample space, called a probability distribution. Show probability distribution table of two dice being rolled.
There are several graphical ways to portray both probabilities and probability distributions. Graphical ways of showing probabilities. There are many models one can use as an introduction to probability, including dice rolls, coin tosses, causes of death, and chances of floods.
Show example. One example is the probability of death due to individual causes. These probabilities can then be used to stimulate a discussion if geologic hazards, impact of risk perceptions, and mathematical calculations of probability. Students have any number of technological tools that they can use to better understand quantitative concepts -- from the calculators in their backpacks to the computers in their dorm rooms.
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