Choose a point at random in a square with sides 0 ? x ? 1 and 0 ? y ? 1. This means that the probability that the point falls in any region within the square is equal to the area of that region. Let X be the x coordinate and Y the y coordinate of the point chosen. Find the conditional probability P(Y < 1/2 | Y > X). (Hint: Draw a diagram of the square and the events Y < 1/2 and Y > X)
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The line y = x divides the square into two equal triangles. The event Y < X corresponds to the area below the line y = x, and the event Y > X corresponds to the area above the line y = x. Since the square is divided into two equal parts by the line y = x, the Show more…
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