Question

a beverage company surveyed 310 customers about their favorite type of weather and preferred beverage. the results are displayed in the table.
is preferring water independent of favoring stormy weather? justify mathematically.
yes, because p(water) = p(water | stormy)
yes, because p(water) = p(stormy | water)
no, because p(water) ≠ p(water | stormy)
no, because p(water) ≠ p(stormy | water)

Explanation:

Step1: Calculate total customers

Total = 28+14+21+7+44+22+33+11+16+18+12+9+36+8+27+4 = 310

Step2: Compute P(water)

P(water) = (28+14+21+7)/310 = 70/310 ≈ 0.2258

Step3: Compute P(water|stormy)

P(water|stormy) = 14/(14+22+18+8) = 14/62 ≈ 0.2258

Step4: Compare probabilities

P(water) = P(water|stormy) ≈ 0.2258

Answer:

Yes, because P(water) = P(water | stormy)