The probability that roger wins a tennis tournament (event a) is 0.45, and the probability that stephan wins the tournament (event b) is 0.40. the probability of roger winning the tournament, given that stephan wins, is 0. the probability of stephan winning the tournament, given that roger wins, is 0. given this information, which statement is true?

events a and b are independent because p(a|b) = p(a).
events a and b are independent because p(a|b) ≠ p(a).
events a and b are not independent because p(a|b) ≠ p(a).
events a and b are not independent because p(a|b) = p(a).