If there are only two possible outcomes to an experiment then...
A.) the two corresponding probabilities must each be.50.
B.) the two corresponding probabilities could be any numbers between 0 and 1, but must add up to 1.
C.) the two corresponding probabilities could each be any numbers between 0 and 1.
D.) the two corresponding probabilities must be 0 and 1.
The sum of all probabilities is always 1, B.
The correct answer is B) the two corresponding probabilities could be any numbers between 0 and 1, but must add up to 1.
When there are only two possible outcomes in an experiment, they are referred to as mutually exclusive events. These two outcomes can be represented as A and B.
In probability theory, the probabilities of these two outcomes are denoted as P(A) and P(B). Since these outcomes are mutually exclusive, the total probability of all outcomes must be equal to 1.
Therefore, the sum of the probabilities of the two outcomes must be 1, which means P(A) + P(B) = 1.
The individual probabilities can be any numbers between 0 and 1 as long as they satisfy the condition of adding up to 1. For example, P(A) could be 0.3 and P(B) could be 0.7, or P(A) could be 0.6 and P(B) could be 0.4.
Hence, option B is the correct choice.