This member does yoga, are they in the weights group?

Question

A gym has 250 members. Their main activity is either weights (100 members) or cardio (150 members). Among the 100 weights members, 45 also attend yoga. Among the 150 cardio members, 30 attend yoga. You pick a member at random and they attend yoga. What is the probability their main activity is weights?

Accepted Answer

The clue "attends yoga" restricts you to yoga-goers, so count them first. - Weights members who do yoga: 45. - Cardio members who do yoga: 30. Total yoga-goers: 45 + 30 = 75. Of those, the weights members number 45: P(	ext{weights} \mid 	ext{yoga}) = \frac{45}{75} = \frac{3}{5} = 0.6. Cardio is the larger group overall, but yoga is more popular among the weights crowd, so among yoga-goers the weights group leads. Takeaway. The right denominator is the yoga subgroup (75), and its split by main activity gives the conditional probability directly.

This member does yoga, are they in the weights group?

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