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?
First find Jack's chances of getting bitten by an infected mosquito: 40% + 20% = 60%
The chance of being infected by a mosquito with after being bitten: 60% * 50% = 30%
Then find the chances of getting ill after receiving the vaccine: 30% * 50% = 15%
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