A box has 20 cards, 10 labelled A and 10 labelled B. Cards drawn with replacement until a second A-card appears. Find the probability the second A-card appears before the third B-card.
Solutions · 1
Official solution
Enumerating sequences ending with the 2nd A before the 3rd B: AA, ABA, BAA, ABBA, BBAA, BABA.
\[P = \frac14+\frac18+\frac18+\frac{1}{16}+\frac{1}{16}+\frac{1}{16} = \frac{11}{16}\]