Question

Which of the following is true regarding the law of total probability.
A. It is a fundamental rule relating marginal probabilities to conditional probabilities.
B. It expresses the total probability of an outcome which can be realized via several distinct events.
C. Both are correct
D. None of these.

Answer 1

Hint: In this problem, we have to find which of the following is true regarding the law of total probability. We can first write the law of total probability, its definition and we can find the correct options from the given following options.

Complete step by step solution:
Here we have to find which of the following is true regarding the law of total probability.
We know that the law of total probability states that,
If \[{{B}_{1}},{{B}_{2}},{{B}_{3}},....\] is a partition of sample space S, then for any event A, we have
\[P\left( A \right)=\sum\nolimits_{i}{P\left( A|{{B}_{i}} \right)P\left( {{B}_{i}} \right)}\]
i.e. the law of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events and hence the name.
The answer is both options A and B.
Therefore, the answer is option C. Both are correct.

Note: We should always remember that the law of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events and hence the name.