On a december day, the probability of snow is .30. the probability of a "cold" day is .50. the probability of snow and "cold" weather is .15. are snow and "cold" weather independent events?

Events A and B are independent if the following holds true:

P(A ∩ B) = P(A) * P(B)

where P(A ∩ B) is the probability of A and B, P(A) is the probability of A, and P(B) is the probability of B.

Setting A = "snow" and B = "cold weather", and plugging in the above numbers will give you the answer.