Niddah 59 - Attending to One's Needs
If a woman was attending to her needs (urinating) and saw blood, then Rabbi Meir resolves it as follows: if she was urinating while standing, she is ritually impure, but if while sitting, she is pure. However, Rabbi Yose says that in either case she is pure.
What is the logic of Rabbi Meir? He says that a woman who is urinating while standing does it out of a pressing need. In her desire to hold the urine back, she might have caused some of it to backwash into the uterus and bring some uterine blood with it. When she was sitting, however, this is not a concern. And Rabbi Yose? He says that the backwashing scenario has a very small probability, and most likely the blood is from a wound in the urinary tract, which does not render her ritually impure.
If a man and a woman urinated into the same basin, and later blood was found in the urine, then Rabbi Yose says that she is ritually pure. If in the case above, where the blood came from a woman, but the source of it was not certain, Rabbi Yose declared her pure, then all the more so here, where it might possibly come from a man, he should declare her pure. That ruling we could have deduced on our own. However, Rabbi Shimon declares her impure, since it is more common for blood to come from a woman.
Art: Daniel Ridgway Knight - Women Washing Clothes By A Stream