If we take 15 then 15c2= 105 and 2/105= 1.9% which is >1% and violating the given rule.
If the win is defined when 2 correct guesses are made , shouldn’t that be in favorable outcome?
The answer given is 15. Could someone please explain why 15 is correct, as per the logic shared above answer should be 50. Can someone please explain what mistake am I making
It should be \frac{1}{\binom{15}{2}} because you’re trying to find one specific, correct pair of letters from a pool of \binom{15}{2} different pairs.
Hi, yes but the question asks about minimum number of letters and not minimum number of pairs so how do we infer that
“to win, a student must correctly guess two random distinct letters…” → one pair out of \binom{15}{2} distinct pairs is the winning condition.
If you don’t feel comfortable with the combinatorics yet, you could just imagine writing it out as \frac{2}{15} \cdot \frac{1}{14}. The first term is \frac {2}{15} because you have 2 choices among a pool of 15 letters. Subsequently, the probability of picking the second term is \frac{1}{14} because there’s only one other correct letter to pick.
okay thanks a lot