Final answer:
The probability that the cricket returns to the leaf where it started after 4 hops is 1/256.
Step-by-step explanation:
The probability that the cricket returns to the leaf where it started after 4 hops can be calculated using the concept of permutations and combinations. We need to find the number of ways the cricket can return to the starting leaf and divide it by the total number of possible outcomes.
Since the cricket randomly hops between 4 leaves, it has a 1/4 chance of returning to the starting leaf after each hop. So, the probability of the cricket returning to the starting leaf after 4 hops is (1/4) * (1/4) * (1/4) * (1/4) = 1/256.
Therefore, the probability that the cricket returns to the leaf where it started after 4 hops is 1/256.