Final answer:
The probability that two randomly selected subsets of the set 1,2,3,4,5 have exactly two elements in their intersection is 5/512.
Step-by-step explanation:
To find the probability that two randomly selected subsets of the set 1,2,3,4,5 have exactly two elements in their intersection, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, we need to calculate how many subsets of size two can be formed from the set 1,2,3,4,5. This can be done using the combination formula, which gives us C(5,2) = 10.
Next, we need to determine the total number of possible outcomes when randomly selecting two subsets from the set. This can be calculated as 2^5 x 2^5 = 2^10 = 1024.
Therefore, the probability is calculated as 10/1024, which reduces to 5/512.