tmua.me Extreme Set B Paper 2 · Question 12

Each use of a machine produces one of the numbers $1$ , $2$ and $3$ . Each number has a fixed positive probability of being produced, and the results of different uses are independent.

If $X$ and $Y$ are the results of two uses, it is known that

\Pr(X<Y)=\frac14,\qquad \Pr(X+Y\text{ is odd})=\frac38.

The machine is used three more times, producing $U$ , $V$ and $W$ .

Given that $U+V+W$ is even, what is the probability that $U$ , $V$ and $W$ are all different?

\dfrac3{32}

\dfrac3{28}

\dfrac3{16}

\dfrac14

\dfrac37

\dfrac3{14}

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tmua.me Extreme Set B Paper 2 · Q12