The probability of getting disease x (event a) is 0.65, and the probability of getting disease y (event b) is 0.76. the probability of getting both disease x and disease y is 0.494. are events a and b dependent or independent?

I would say independent since the problem doesn't state any relation between disease X and disease Y. Also I beleive if it were dependent the probability of getting both wouldn't be .494 (which is .65 *.76). It would have to be probability of event A and event B, and then divided by probability of just B