Question: In this exercise, you are asked to verify that the sum of the joint probabilities in a row or column of a joint probability distribution

In this exercise, you are asked to verify that the sum of the joint probabilities in a row or column of a joint probability distribution equals the marginal probability in that row or column. Consider the following joint probability distribution.
align="center">In this exercise, you are asked to verify that the

a. Explain why
R1 = (R1 & C1) or ····· or (R1 & Cn)
b. Why are the events (R1 & C1), . . . , (R1 & Cn) mutually exclusive?
c. Explain why parts (a) and (b) imply that
P(R1) = P(R1 & C1)+ ··· + P(R1 & Cn).
This equation shows that the first row of joint probabilities sums to the marginal probability at the end of that row. A similar argument applies to any other row or column.

Cn P(Ri) RPIR P(Cn)

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