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There are two main methods: theoretical and empirical.
The first of these is used when there is a relatively simple model for the possible outcomes of a trial. For example, if you roll a fair die, laws of physics suggest that each of the six faces is equally likely to end up on the top face. The probability for each of the six numbers is, therefore, 1/6.
The second method is used when there is no satisfactory model based purely on theory: if you have a loaded die, for example. It may, just about, be possibly to analyse the physical properties of the mass distribution within the coin and develop an appropriate model for the outcome of a throw. However, it is simpler to use the second method. Given the chance, roll the die again and again (and again and again and ... ) and record the outcomes. The probability of any particular outcome is the proportion of the trials that result in that particular event. Thus, if a loaded die comes up 6 fifty times out of 200 throws, then the probability of throwing a 6 is 50/200 = 0.25.
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What is used to determine the probability of two indepepdent events occurring?
Multiply together the probability that each event would have of occurring by itself. For example, the probability of rolling a "3" on a single die is 1/6 ,because there are 6 different possibilities. And the probability of flipping a "heads" on a coin is 1/2 , because there are two possibilities. Then the probability of rolling a "3" AND flipping a "heads" is ; 1/6 x 1/2 = 1/12 .
Example of joint probability?
Joint probability is the probability that two or more specific outcomes will occur in an event. An example of joint probability would be rolling a 2 and a 5 using two different dice.
If you roll two dice what is the probability of the event that you roll a total of five on the two dice?
uummm!!!! The probability would maybe close to 5 or 4. * * * * * The answer is clearly incorrect because the probability of an event cannot be greater than 1. The actual probability, assuming the dice are fair, is 4/36 = 1/9 = 11.11...%
Can probability be expressed as a percent?
Yes, probability can be expressed as a percent. It is common to express probabilities as a percentage, which is calculated by multiplying the probability by 100. For example, if the probability of an event is 0.25, it can also be expressed as 25%.
Which would be more useful in finding the probability of an event a tree diagram or the counting principle?
The answer depends on the nature of the event. If the event is composed of sub-events then a tree diagram may help but if not, it is irrelevant.
