yes.
Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.
The probability is always a fraction except when it is 0 or 1. If a probability = 1 then it will definitely happen. If the probability is 0 then it will not happen. If you toss a fair coin the probability of heads is 1/2, and the probability of tails is 1/2. These fractions are representations of the probabilities. Not all fractions are representative of probabilities. Fractions can be used to represent a portion of a whole. Like what portion of a class is boys, and what portion is girls: If there are 8 boys and 7 girls, then the 8/15 of the class is boys, and 7/15 of the class is girls.
No, but it can represent the probability of such an outcome.
Since 5/4 > 1, it cannot represent a probability of an event A, denoted by Pr(A), because for any event A, 0 ≤ Pr(A) ≤ 1. If A never occur, then Pr(A) = 0; if A always occur, then Pr(A) = 1.
yes.
Continuous
No, 0.006 is not a valid probability because probabilities must be between 0 and 1. In this case, 0.006 is less than 0 and therefore cannot represent a probability.
False.
Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.
The probability is always a fraction except when it is 0 or 1. If a probability = 1 then it will definitely happen. If the probability is 0 then it will not happen. If you toss a fair coin the probability of heads is 1/2, and the probability of tails is 1/2. These fractions are representations of the probabilities. Not all fractions are representative of probabilities. Fractions can be used to represent a portion of a whole. Like what portion of a class is boys, and what portion is girls: If there are 8 boys and 7 girls, then the 8/15 of the class is boys, and 7/15 of the class is girls.
Assuming you mean random variable here. A random variable is term that can take have different values. for example a random variable x that represent the out come of rolling a dice, that is x can equal 1,2,3,4,5,or 6. Think of probability distribution as the mapping of likelihood of the out comes from an experiment. In the dice case, the probability distribution will tell you that there 1/6 the time you will get 1, 2,3....,or 6. this is called uniform distribution since all the out comes have that same probability of occurring.
It can represent anything that you want - provided that you define it as such. Here are some examples:Algebra: it could represent a typical element in the set of rational numbers.Geometry: In the Cartesian plane (or space), it could represent the ordinate (second coordinate) of a point.Probability: It could represent the probability of the complement of a given event - particularly for the binomial distribution.
Probabilities are expressed a few different ways, often depending on the means of calculating the probability.Theoretical probabilities are generally calculated as the number of successes divided by the total number of possibilities. For example, rolling a number greater than 4 on a die has two successes (5 or 6) and six possibilities (1, 2, 3, 4, 5, or 6). Because each of these outcomes is equally likely to occur, the probability is 2/6 = 1/3. Probabilities calculated in this way are typically expressed as fractions, although they can also be expressed as decimals or percents (more commonly referred to as the chance of an event occurring).Probabilities based on the normal curve, models, random variables and the like are generally expressed as decimals, although percentages are also acceptable.Note that for all of these forms, probabilities are always between 0 and 1 inclusive (0% and 100%). A probability of 0 (0%) has absolutely no chance of occurring while a probability of 1 (100%) means an event is certain to occur. Probabilities in between represent a certain degree of likelihood of the event occurring.
Calculating Probabilities for Equally Likely OutcomesStep 1: Count the total number of possible outcomes of an eventStep 2: Count the number of outcomes that represent a success - that is, the number of outcomes that represent the desired result.Step 3: Determine the probability of success by dividing the number of successes by the total number of possible outcomes:
yes
The probability of inclusive events A or B occurring is given by P(A or B) = P(A) + P(B) - P(A and B), where P(A) and P(B) represent the probabilities of events A and B occurring, respectively.