数学问题概率求解释

题目

数学问题概率求解释
Rework problem 28 from section 3.4 of your text, involving the drawing of two
balls from a box of colored balls. Assume the box contains 8 balls:
3 red, 3 blue, and 2 yellow. A ball is drawn and its
color noted. If the ball is yellow, it is replaced; otherwise, it is not.
A second ball is then drawn and its color is noted.
What is the probability that the first ball was yellow, given that the
second was red?

KEY IS 7/27
Anyone know the detailed process?
Thax!

答案

首先算出来取出第二个求是红球的概率：3/8*2/7+3/8*3/7+2/8*3/8=81/(28*8)
再算出第一次取出黄球第二次取出红球的概率：2/8*3/8=6/(8*8)
6/(8*8)除以81/(28*8)就是7/27
ps：中间数字太大我就没算结果了