Conditional Probability and Independence: Uses 1

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Page 1 - Calculating Conditional Probability: Dependent Events

Make sure you understand these points before you move on:

How to calculate conditional probability.

How to identify dependent and independent events.

Example - Finding the Probabilities for Learning Styles

Of the 3329 females and 1933 males who took the Diablo Valley College Learning Styles Survey in the spring of 1999, here are the data for students who prefer the Auditory learning style:

Learning Styles	Auditory	Total
Female	1002	3329
Male	740	1933
Total	1742	5262

Is the Auditory learning style dependent on gender?

For the entire group, the Auditory learning style's relative-frequency is:

P(Auditory) = (all auditory)/(entire group) = 1742/5262 = 0.331

To calculate conditional probabilities we restrict our calculations to each sub-group:

Females:
P(Auditory given Female) = (Auditory and female)/ (total females)
P(Auditory | Female) = 1002 /3329 = 0.301

Males:
P(Auditory given Male) = (Auditory and male)/ (total males)
P(Auditory | Male) =740/1933 = 0.383

For this group, men are more likely than women to prefer the Auditory learning style.

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