Among a dozen eggs, three are rotten. A cookie recipe calls for two eggs; they'll be selected randomly from that dozen. Which plan could be used to simulate the number of rotten eggs that might be chosen?
I. Let 0,1 , and 2 represent the rotten eggs, and $3,4 , \ldots , 11$ the good eggs. Generate two random numbers $0 - 11$, ignoring repeats.
II. Randomly generate a 0,1 , or 2 to represent the number of rotten eggs you get.
III. Since $25 \%$ of the eggs are rotten, let $0 =$ rotten and $1,2,3 =$ good. Generate two random numbers $0 - 3$ and see how may 0 's you get.
A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

Question

Quizplus · Accepted Answer

Plan I accurately simulates the selection process by assigning unique numbers to each egg and ensuring that the proportion of rotten to good eggs is correct. Plan II does not account for the actual distribution of eggs and their selection process. Plan III inaccurately represents the probability of selecting a rotten egg, as it simplifies the situation to a 25% chance per selection without considering the reduction in total eggs after the first selection.

Among a Dozen Eggs, Three Are Rotten 3,4,…,113,4 , \ldots , 113,4,…,11

Among a Dozen Eggs, Three Are Rotten $3,4 , \ldots , 11$