A box contains six white stones and six black stones. Peter selects three stones at random without replacement. Let Y be the random variable that

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A box contains six white stones and six black stones. Peter selects three stones at random without replacement. Let Y be the random variable that represents the number of white stones minus the number of black stones drawn.

(i) What is the range of values of Y?

(ii) Write down the probability function of Y.

(iii) Suppose for each white ball drawn, Peter wins $2 while for each black ball he loses $1.50. What is his expected profit from this experiment?

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