tmua.me Extreme Set C Paper 1 · Question 17

Six counters initially carry the numbers

1,\quad2,\quad3,\quad4,\quad5,\quad7.

At each stage, one pair of the counters currently present is chosen uniformly at random. The chosen counters are removed and replaced by one counter carrying their sum. The process stops when two counters remain.

Given that the final two numbers are equal, what is the probability that the first pair chosen carried $1$ and $2$ ?

\dfrac1{15}

\dfrac1{14}

\dfrac1{16}

\dfrac4{49}

\dfrac47

\dfrac1{28}

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tmua.me Extreme Set C Paper 1 · Q17