40% of the mosquitos in Jack's area are infected with malaria. 20% of the mosquitos are infected with Zika virus. Without a vaccine, the chances of getting infected with either virus after getting bitten by an infected mosquito are 50%. Jack is taking an experimental malaria vaccine that reduces the chances of getting infected after getting bitten by 50%. If Jack gets bitten by a random mosquito, what is the percentage chance he catches either Zika virus or malaria?
Please reason step by step, and put your final answer within \boxed{}.
user