From the basic formula of the elementary probability formula

    P(snow OR a traffic jam) = P(snow) + P(a traffic jam) - P(snow AND a traffic jam).     (1)



Substitute the given data into this formula.  You will get

    0.82 = 0.8 + 0.10 - P(snow AND a traffic jam).          (2)



From this equation

    P(snow AND a traffic jam) = 0.8 + 0.1 - 0.82 = 0.08.    (3)



From the other hand side,

   P(snow) * P(a traffic jam) = 0.1 * 0.8 = 0.08.           (4)



From (3) and (4),  we see that  

    P(snow AND a traffic jam) = P(snow) * P(a traffic jam).



From the definition of independent events, it means tha the events  "it snows" and "a traffic jam occurs" independent.