Question

If I pick 5 letter of the alphabet and I chose another person to pick 6 letter from the alphabet. If any of mine match the other persons letters I win. I none match I lose. Why is there a 72 percent chance of me winning?

Answer 1

compute the probability that the other person wins
she has to pick letter, without replacement that do not match your five
say you pick a, b, c, d, e
then the probability she doesn't pick your letters is
\[\frac{21}{26}\times \frac{20}{25}\times \frac{19}{24}\times \frac{18}{23}\times \frac{17}{22}\times \frac{16}{21}\]

Answer 2

^nice. P(you win) = 1 - P(other person wins)

Answer 3

could also say i guess that the probability the other person wins is
\[\binom{21}{26}\] same thing i suppose