Multiplication Principle of Counting
Probability
That's the 'probability' of a favorable outcome.but only if the outcomes are equally likely.
Theoretical probability is the probability of an event when all outcomes are equally likely. With theoretical probability, you determine the probability by dividing the number of ways the event can occur by the total number of equally likely outcomes.
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The probability of an event is the number of outcomes that are favourable to the outcome divided by the total number of outcomes. For continuous variables, it is the proportion of the outcome space, but the same argument applies.The number of favourable outcomes must be non negative and so the probability has to be greater than or equal to 0. Also, the number of favourable outcomes can, at most, be as large as the total number so the probability must be less than or equal to 1.
Counting Principle is used to find the number of possible outcomes. It states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are mn possible outcomes for the two events together.
The number of possible outcomes that matches the event divided by the total number of possible outcomes is the probabilityof that event.
Probability
number of outcomes divided by the number of ways of occurrence
probability
The probability of an event occurring can be found by dividing the number of favorable outcomes (what you want to happen) by the number of possible outcomes number of favorable outcomes probability = _________________________ number of possible outcomes
That's the 'probability' of a favorable outcome.but only if the outcomes are equally likely.
The probability of an event is the number of favourable outcomes divided by the total number of possible outcomes. What is the total number of possible outcomes of tossing a number cube? 6 How many outcomes are favourable to the event of getting a five? 1 So the prob is 1/6 or 0.16667
If you can enumerate the outcome space into equally likely events, then it is the number of outcomes that are favourable (in which the event occurs) divided by the total number of outcomes.
For any event, the complementary event is all of the other possible outcomes. For an event (Rolling a number cube) " Rolling an odd number " The complementary event is " Rolling an even number "
The probability of an event is the ratio of the number of equally likely oucomes of a trial which are favourable to that event, and the total number of outcomes.
If the events are independent then you can multiply the individual probabilities. But if they are not, you have to use conditional probabilities.