What are the odds of picking two pre-selected non-sequential letters in order out of a $26$ letter alphabet, i.e. $D$ then $S$, not $S$ then $D$? One chance only.
[Math] Mathematical odds of picking letters
probability
probability
What are the odds of picking two pre-selected non-sequential letters in order out of a $26$ letter alphabet, i.e. $D$ then $S$, not $S$ then $D$? One chance only.
Best Answer
if I understand the question correctly, what's the probability that you select a two letters from the English alphabet, such that the second one comes after the first. Use the law of total probability: $$ P(X) = \sum_{k=1}^{26}P(X|Y=k)P(Y=k) = \frac{25}{26} \cdot P(X=A) + \frac{24}{26} \cdot P(X=B) +\ldots $$
of course $P(X=j) = \frac{1}{26}$. Can you handle from here?
EDIT: you may want ot use the identity $\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$