We have 12 puppies where we have 5 poodles (P), 3 terriers (T) and 4 retreivers (R).
If the selection is with replacement, the probabilities of the two events (Rebecka selection and Aaron selection) are independent.
The probability that Rebecka selects a terrier is 3 in 12, as there are only 3 terriers between the 12 puppies.
In the same way, and as the puppy selected by Rebecka is replaced with the same type, the probability that Aaron selects a retriever is 4 in 12.
Then, the probability of the two events is equal to the product of the probabilities of each event:
![P(\operatorname{Re}=T,A=R)=P(\operatorname{Re}=T)\cdot P(A=R)=(3)/(12)\cdot(4)/(12)=(1)/(4)\cdot(1)/(3)=(1)/(12)]()
Answer: the probability that Rebecka selects a terrier and Aaron selects a retriever is P=1/12.