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In a college, 25 % of the boys and 10 % of the girls offer Mathematics. The girls constitute 60 % of the total number of student. If a student is selected at random and is found to be studying Mathematics, the probability that the student is a girl, is
The probability that a student studying Mathematics is a girl is 3/8.
Total students studying: 100 Boys: 40% of 100 = 40 Girls: 60% of 100 = 60
Given that:
- 25% of boys offer Mathematics: 0.25 * 40 = 10 boys
- 10% of girls offer Mathematics: 0.10 * 60 = 6 girls
So, the total number of students offering Mathematics = 10 boys + 6 girls = 16 students.
Therefore, the probability that a student studying Mathematics is a girl is 6/16 = 3/8.
What is Probability Theory?
Probability theory is a branch of mathematics concerned with quantifying uncertainty and randomness. It provides a framework for analyzing and predicting the likelihood of different outcomes in various situations where randomness plays a role. Probability theory deals with the study of random events, experiments, and processes, and it allows for the formalization of uncertainty through mathematical models.
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Key concepts in probability theory include:
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Probability: Probability is a measure of the likelihood that an event will occur. It is typically expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Intermediate values represent degrees of likelihood between these extremes.
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Random Variables: A random variable is a variable that can take on different values as a result of random processes or outcomes. It can be discrete, assuming a finite or countably infinite set of possible values, or continuous, taking on any value within a specified range.
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Probability Distributions: Probability distributions describe how the probabilities are distributed over the possible values of a random variable. Common distributions include the uniform distribution, normal distribution, binomial distribution, and Poisson distribution, among others.
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Events and Sample Spaces: An event is a set of outcomes of an experiment to which a probability is assigned. The sample space is the set of all possible outcomes of the experiment. Events are subsets of the sample space.
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Conditional Probability: Conditional probability is the probability of an event occurring given that another event has already occurred. It is expressed as P(A|B), the probability of event A occurring given that event B has occurred.
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Independence: Events are considered independent if the occurrence of one event does not affect the probability of the other event occurring.
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Bayes’ Theorem: Bayes’ theorem is a fundamental theorem in probability theory that describes the probability of an event based on prior knowledge of conditions that might be related to the event.
Probability theory has applications in various fields such as statistics, physics, economics, engineering, and computer science. It is used to model uncertainty, make predictions, analyze data, and make decisions under uncertainty.
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Source: Math Hello Kitty
Categories: Math
