OG17 Math Review Arithmetic关于概率的一个问题

ET游戏狂

For a final example of some of these rules, consider an experiment with events A, B, and C for which
P (A) = 0.23, P (B) = 0.40, and P (C) = 0.85. Also, suppose that events A and B are mutually exclusive
and events B and C are independent.
Note that P (A or C) and P (A and C) cannot be determined using the information given. But it
can be determined that A and C are not mutually exclusive since P (A) + P (C) = 1.08, which is
greater than 1, and therefore cannot equal P (A or C); from this it follows that P (A and C) ≥ 0.08.
One can also deduce that P (A and C) ≤ P (A) = 0.23, since is a subset of A, and that
P (A or C) ≥ P (C) = 0.85 since C is a subset of . Th us, one can conclude that
0.85 ≤ P (A or C) ≤ 1 and 0.08 ≤ P(A and C) ≤ 0.23.
不理解的是为什么A和C同时发生的概率不是0.23*0.85=0.1955而是一个范围呢？既然不是mutually exclusive那就是independent，A和C independent不就是A*C吗？ 谁能帮忙解答下？

huntfrank

不互斥不等于独立。