Question

Let the following rules be separately written down on three pieces of paper: f1 (x1, x2, x3) = 4 max {x1, x2} f2 (x1, x2, x3) = x1 + x2 + 3x3 f3 (x1, x2, x3) = 2x1 + 2 max {x2, x3}. One of these pieces of paper will now be drawn blindly. Then, a coin will be thrown three times and the result will be assigned as follows: Number = 0, Head = 1 An ordered tuple (x1, x2, x3) ∈ {0, 1}^3 will be assigned based on the coin toss results (first roll results in x1, etc.). Then, the drawn mapping rule will be applied to the result of the coin toss (x1, x2, x3). The result of this procedure is given by the random variable X, and the result of drawing the formula is described by Y. Y has the range of values {f1, f2, f3}. Determine P(Y = fj | X = 4) for j = 1, 2, 3 respectively.

          Let the following rules be separately written down on three pieces of paper:
f1 (x1, x2, x3) = 4 max {x1, x2}
f2 (x1, x2, x3) = x1 + x2 + 3x3
f3 (x1, x2, x3) = 2x1 + 2 max {x2, x3}.
One of these pieces of paper will now be drawn blindly. Then, a coin will be thrown three times and the result will be assigned as follows:
Number = 0, Head = 1
An ordered tuple (x1, x2, x3) ∈ {0, 1}^3 will be assigned based on the coin toss results (first roll results in x1, etc.).
Then, the drawn mapping rule will be applied to the result of the coin toss (x1, x2, x3). The result of this procedure is given by the random variable X, and the result of drawing the formula is described by Y.
Y has the range of values {f1, f2, f3}. Determine P(Y = fj | X = 4) for j = 1, 2, 3 respectively.

Added by Parker S.

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