A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consecutive digits of the number is prime is

The prime digits are 2, 3, 5, 7. If we fix 2 at first place, then other 2n - 1 places are filled by all four digits. So the total number of cases is 42n-1.Now, sum of 2 consecutive digits is prime when consecutive digits are (2,3) or (2, 5).Then 2 will be fixed at all alternative places.So favorable number of cases is 2n. Therefore, probability is2n42n−1=2n2−4n+2=222−3n=423n