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?
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.