Of 12 eggs, two are rotten. Four are chosen randomly. Then four more are chosen randomly from the remaining 8. Find the conditional probability that the second batch of 4 were all good given that at best one of the first 4 was rotten.
Of 12 eggs, two are rotten. Four are chosen randomly. Then four more are chosen randomly from the remaining 8. Find the conditional probability that the second batch of 4 were all good given that at best one of the first 4 was rotten.
Let X be the random variable 'number of rotten eggs in first sample'.
X ~ Hypergeometric(N = 12, n = 4, D = 2).
Let Y be the random variable 'number of rotten eggs in second sample'.
Y ~ Hypergeometric(N = 8, n = 4, D = either 0, 1 or 2 depending on X).
What does "at best one of the first 4 was rotten" mean? Does it mean there was at least 1 rotten egg in the first four ....? Assuming it does, then you need to calculate $\displaystyle \Pr(Y = 0 | X \geq 1)$.
But you will need to get clarification on this before the question can be done with certainty.