ProbabilityHard
Question
A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime, is
Options
A.4 × 23n
B.4 × 2-3n
C.23n
D.none of these
Solution
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 total number of cases = 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 favourable cases = 2n
Therefore probability =
= 2n . 2-4n+2 = 22 . 2-3n = 
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