Suppose this diagram illustrates the number of women and Democrats in the U.S. Senate. We can see that 22 of the senators are women and 40 of the senators are democrats. since there are
100 senators this means that the probability of a senator being a woman is 0.22 and the probability
of a senator being a democrat is 0.4. If we try to use the addition rule, we'd conclude that the
probability of a senator being a woman or a Democrat is 0.22 + 0.4 = 0.62. How can we be sure that
this is incorrect?

Question

Suppose this diagram illustrates the number of women and Democrats in the U.S. Senate.  We can see that 22 of the senators are women and 40 of the senators are democrats. since there are
100 senators this means that the probability of a senator being a woman is 0.22 and the probability
of a senator being a democrat is 0.4. If we try to use the addition rule, we'd conclude that the
probability of a senator being a woman or a Democrat is 0.22 + 0.4 = 0.62. How can we be sure that
this is incorrect?

Quizplus · Accepted Answer

The Answer of Suppose this diagram illustrates the number of women and Democrats in the U.S. Senate.  We can see that 22 of the senators are women and 40 of the senators are democrats. since there are
100 senators this means that the probability of a senator being a woman is 0.22 and the probability
of a senator being a democrat is 0.4. If we try to use the addition rule, we'd conclude that the
probability of a senator being a woman or a Democrat is 0.22 + 0.4 = 0.62. How can we be sure that
this is incorrect?

Suppose This Diagram Illustrates the Number of Women and Democrats