Let K be a discrete random variable that can take the values 1, 2, and 3, all with equal probability. Suppose that X takes values in [0, 1] and that for x in that interval we have fxIk^(x I k) = { 1, if k = 1,
2x, if k = 2,
3x, if k = 3.
Find the probability that K = 1, given that X = 1/2.

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step-by-step explanation:

could you provide figure.

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15