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" Raw eggs have a 1/20,000 probability of having salmonella. If you eat two raw eggs what is the probability that you ate a raw egg with salmonella."

The online answer he gives:

"For this question you need the sum rule because if either egg has salmonella you will get sick.

prob(egg1)+prob(egg2)-prob(egg1) x prob(egg2) or

1/20000+1/20000-(1/20000)*(1/20000)=39,999/400,000,000 or a hair under 1/10000

I think I understand this.( you subtract probability of both eggs having salmonella)

But when I calculate getting ONE six throwing a pair of dice using this method I get

1/6+1/6-(1/6*1/6)=11/36.

This is the wrong answer.

The answer should be 10/36. Somebody told me you have to subtract 1/36 twice.If so why do you do it only once with eggs