3 Cards Drawn: Three of a Kind
From a standard 52‐card deck, 3 cards are drawn. What is the probability that all three cards share the same rank?
Answer
The first card can be anything. Once that card is chosen, there are 51 remaining cards, 3 of which match the first card’s rank. Hence the probability the second card matches the first card’s rank is
\[
\frac{3}{51}.
\]
Now 50 cards remain, and only 2 of them match that same rank, giving a probability
\[
\frac{2}{50}
\]
that the third card also matches the rank.
Multiplying these together,
\[
\frac{3}{51} \;\times\; \frac{2}{50}
\;=\;
\frac{6}{2550}
\;=\;
\frac{1}{425}
\;\approx\;
0.00235
\;\text{(about }0.235\%\text{).}
\]