People seem to be confusing the odds of getting sick with the odds of getting sick if you are infected. The odds of getting infected are multiplied by the odds of suffering from the disease if infected to arrive at the total odds of suffering from the disease. The 95% immunity is the probability of not suffering if exposed to the virus (5% chance of becoming ill or 1 in 20). The vaccine doesn’t prevent you from becoming infected—it reduces the chances by 95% of feeling miserable or dying once infected.
So, if the chances of becoming exposed to the virus so that you carry it around were, say, 1 in 1,000, the total odds of getting sick are 1 in 1,000 times 1 in 20 or 1 in 20,000. If people refuse to take sensible precautions, then the odds of getting infected go up as do the odds of suffering.
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