In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 56% majored in business or commerce; 15% majored in engineering; 15% majored in the social sciences; 7% majored in the sciences; 4% majored in the humanities; and 3% listed some major other than the preceding. Assume there are no double majors. (a) What percent of those who took the test in this certain year majored in either engineering or the sciences? (Enter your answer as a percent and as a whole number.) ?= % Select the probability rule you used to find the answer. Rule 3.3. Two events ?A and ?B are disjoint if they have no outcomes in common and so can never occur together. If ?Aand ?B are disjoint, ?(? or ?)=?(?)+?(?).P(A or B)=P(A)+P(B). Rule 4.4.For any event ?,A, ?(? does not occur)=1−?(?).P(A does not occur)=1−P(A). Rule 2.2. If ?S is the sample space in a probability model, then ?(?)=1.P(S)=1. Rule 1.1. The probability ?(?)P(A) of any event ?A satisfies 0≤?(?)≤1.0≤P(A)≤1. (b) What percent of those who took the test in this certain year majored in something other than business or commerce? (Enter your answer as a percent and as a whole number.) ?=P= % Select the probability rule you used to find the percentage of undergraduates who majored in something other than business or commerce. Rule 4.4. For any event ?,A, ?(? does not occur)=1−?(?).P(A does not occur)=1−P(A). Rule 1.1. The probability ?(?)P(A) of any event ?A satisfies 0≤?(?)≤1.0≤P(A)≤1. Rule 3.3.Two events ?A and ?B are disjoint if they have no outcomes in common and so can never occur together. If ?Aand ?B are disjoint, ?(? or ?)=?(?)+?(?).P(A or B)=P(A)+P(B). Rule 2.2. If ?S is the sample space in a probability model, then ?(?)=1.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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