What Is The Probability That You End Up With An A?

What is the probability that you end up with an A?

You will take either a basket-weaving course or a philosophy course, depending on what your advisor decides. The probability that your advisor chooses the basket-weaving course is 10%, and the probability that they choose the philosophy course is 90%. The probability of earning an A if you take basket weaving is 0.85, and the probability of earning an A if you take philosophy is 0.60. To find the overall probability that you end up with an A, we need to consider the law of total probability, which accounts for all possible scenarios weighted by their respective probabilities.

The probability that you take basket weaving and earn an A is 0.10 (probability of choosing basket weaving) multiplied by 0.85 (probability of earning an A in basket weaving), which is 0.085. Similarly, the probability that you take philosophy and earn an A is 0.90 (probability of choosing philosophy) multiplied by 0.60 (probability of earning an A in philosophy), which is 0.54. Adding these two probabilities gives the total probability of ending up with an A:

0.085 + 0.54 = 0.625.

Therefore, the probability that you end up with an A is 0.625, or 62.5%.

Paper For Above instruction

In this analysis, we explore the probability of obtaining an A in a scenario where a student’s course assignment is determined by the advice of an academic advisor. The decision involves two possible courses: basket weaving and philosophy. The calculations incorporate conditional probabilities based on the likelihood of the advisor choosing each course and the probability of achieving an A within each course. This case illustrates the application of the law of total probability, a fundamental concept in probability theory that allows for the calculation of overall probabilities when dealing with mutually exclusive scenarios.

Given that the advisor selects the basket-weaving course with a probability of 0.10 and the philosophy course with a probability of 0.90, and that the probability of earning an A in basket weaving is 0.85 while in philosophy it is 0.60, we set out to find the total probability of the student ending up with an A. The calculation involves multiplying the conditional probability of earning an A given each course by the probability of being assigned to that course and summing the results. This method effectively weighted averages the conditional probabilities by their respective probabilities of occurring, providing a comprehensive measure of success probability.

The calculation confirms that the probability of achieving an A in this context is 0.625. This insight highlights how probabilistic reasoning can inform expectations in uncertain decision-making scenarios, such as course selection influenced by an advisor. Moreover, understanding these probabilities can help students and educators assess the likelihood of success based on different courses and the advisor’s preferences, which may influence student planning and academic advising strategies.

References

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