Oracle's Riddle

By choice, we have four scenarios of whether we'll meet the soul mate today and whether we'll meet tomorrow, as shown above. Note that the red legs (no meeting today choice) have $y + (1-y) = 1 =100\%$ .

Let $x$ be the chance of meeting the soul mate today and $y$ be the chance of meeting her tomorrow if we don't see her today. Thereby, the chance will be doubled to $2y$ if we see her today.

Likewise, if we don't see her today, the chance of not seeing her tomorrow will be $1-y$ , complemented to $y$ . This chance is three times that of $1-2y$ , another complement to $2y$ .

Thus, $1-y = 3(1-2y) = 3-6y$ . $y = 0.40 = 40\%$ .

Then $52\% = x(2\times 40\%) + (1-x)(40\%) = (40\%)x +(40\%)$ .

$12\% = (40\%)x$

$x = \boxed{30\%}$ .

$$ Checking for tomorrow's no meeting chance = $(30\%)(100\%-80\%) + (70\%)(100\%-40\%) = 6\% + 42\% = 48\%$ , complementing the original $52\%$ in the question.