Competition problem — Combinatorics

Library / /5 of 520

Combinatorics Difficulty 5.4 AIME, harder Find the answer

Question (3): As shown in Figure 3, if $F D$ is connected, what is the probability that it reaches $D$ ?

untranslated part:

(3) : 如图 3 所示, 如果 $F D$ 是相连的, 它色到 $D$ 处的概率是多少?

translated part:

(3): As shown in Figure 3, if $F D$ is connected, what is the probability that it reaches $D$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solve: The probability that it slinks to $D$ is $\frac{1}{2} \times \frac{1}{4}+\frac{1}{2} \times \frac{1}{2}=\frac{3}{8}$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.