The student body of 3, 191 students has been split up into three categories: Tho

Question

The student body of 3, 191 students has been split up into three categories: Those who prefer the cafeteria food (914), those who prefer the Den food (1075), and those who prefer to cook for themselves (1202). Out of the cafeteria lovers, the probability of them meeting the recommended daily step count of 10, 000 is 30%. Out of the den lovers, the probability of them meeting the recommended daily step count is 25%. Out of the chefs, the probability of NOT meeting the step count is 26%. What is the probability that a selected student is a Den-lover, given that they met their step count? Show all of your work.

Explanation / Answer

probability of meeting their step count =(914/3191)*0.3+(1075/3191)*0.25+(1202/3191)*0.74=0.4489

hence probabilty that he/she is den lover given meeting step count =(1075/3191)*0.25/0.4489 =0.1876

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