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## Homework Statement

One box of eggs has 12 eggs. The probability of all eggs being good is 70%. The probability of one being bad is 20%. The probability of two being bad is 10%. Given that 2 randomly selected eggs are good, what is the probability that all the eggs will be good?

## Homework Equations

## The Attempt at a Solution

According to bayes theorem,

P(all good | random 2 are good) = ( P(random 2 are good | all good) * P(all good) ) / P(random two are good)

Now, P(random 2 are good | all good) = P(random 2 are good <and> all good) / P(all good)

=> " P(random 2 are good <and> all good) " are dependent events. Can't seem to figure out how to get around this.