Well... the probabilities should add up to exactly 1 and cannot be negative.
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No. The Normal distribution is symmetric: skewness = 0.
The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
If the two distributions can be assumed to follow Gaussian (Normal) distributions then Fisher's F-test is the most powerful test. If the data are at least ordinal, then you can use the Kolmogorov-Smirnov two-sample test.
8=D
More information is needed to determine the answer to the question. We need to know the probability of success or failure.