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.
You add when you're combining different groups or categories of items, such as when calculating the total number of possible outcomes from different events. You multiply when you're determining the total number of outcomes from multiple independent events happening simultaneously, as each outcome in one event can pair with outcomes in another. For example, if you have two dice, you would multiply the number of sides on each die (6 x 6) to find the total number of possible outcomes.
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 total number of possible outcomes of a compound event can be determined by multiplying the number of possible outcomes of each individual event. This is based on the fundamental principle of counting, which states that if one event can occur in (m) ways and a second event can occur independently in (n) ways, the two events together can occur in (m \times n) ways. This multiplication applies to any number of independent events, allowing for a systematic way to calculate the total outcomes for more complex scenarios.
The number of possible outcomes that matches the event divided by the total number of possible outcomes is the probabilityof that event.
Probability
probability
number of outcomes divided by the number of ways of occurrence
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
The event described is known as a probability event. In this context, the ratio represents the likelihood of a specific outcome occurring compared to all possible outcomes in a given scenario. This ratio can be expressed as a fraction, where the numerator is the number of favorable outcomes for the event, and the denominator is the total number of possible outcomes. Probability values range from 0 (impossible event) to 1 (certain event).
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.