Changing Probabilities into Conditional Probabilities

Changing Probabilities into Conditional Probabilities

In statistics, probability defines the likelihood of an event occurring, which falls between values 1 and 0, with 1 representing the certainty that an event will occur and 0 representing the certainty that an event will not occur. One of the types of probability is conditional probability, which represents the probability of one event occurring given that the other event occurred (Bissiri & Walker, 2018). For instance, in a classroom situation, male and female students may have different performance trends and abilities. The grades and genders of the students can be analyzed as conditional probabilities. By categorizing the performance in grades, we can find the probability of a randomly selected student attaining a certain grade, given that the student belongs to a particular gender. The contingency table for the conditional probabilities can be presented as follows;

	A	B	C	Total
Female	6	15	8	29
Male	8	13	14	35
Total	14	28	22	64

From the table, we can generate several probabilities using the formula in Black (2019). For instance, we can calculate the probability that a student selected randomly will be female given that they attained a grade A in their overall semester grades.

Conditional Probability Formula= P(E1/E2) = P(E1 and E2)/ P(E2)

Where; P(E1/E2) = Probability of Event 1 given E2 occurred

P(E1 and E2)= Probability of Event 1 and Probability of event 2

Therefore, P(F/A)= P(F and A)/ P(A)

= (6/64)/ (14/64) = 0.09375/0.21875= 0.428

From this probabilistic condition, we can calculate probabilities for different events occurring. One of the questions that can be posed from the table regarding the conditional probability of the exemplified event is: What is the probability that a student selected randomly will be a male given that they attained a grade C in their overall semester grades?

References

Bissiri, P. G., & Walker, S. G. (2018). A Definition of Conditional Probability with Non-Stochastic Information. Entropy (Basel). 3;20(8):572. doi: 10.3390/e20080572.

Black, K. (2019). Business Statistics: For Contemporary Decision Making. (10th Edition). Wiley Global Education US.

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Changing Probabilities into Conditional Probabilities
Describe a situation where you see probabilities or might see probabilities. Then, present this probability as a conditional probability.

Make assumptions about the conditional probability table that could accompany such a situation and pose a question for a specific probability.
References:
1. Black, Ken. Business Statistics: For Contemporary Decision Making. (10th Edition). Wiley Global Education US, 2019.