Question

袋中装有大小相同的5个红球和3个黄球,从中任取2个1)取出两个红球概率（2）取出两个颜色相同的球概率

Answer 1

首先你要明确概率公式：

概率 = 满足条件排列÷全排列

下面C(a,b)表示从b个对象中任取a个的组合数

另外,组合公式为 C(a,b) = b!/[a!(b-a)!]

（1）满足条件排列数 = C(2,5) = 5!/(2!3!) = (5!/3!)/2! = 5*4/2 = 10

全排列 = C(2,8) = 8!/(2!6!) = (8!/6!)/2! = 8*7/2 = 28

∴所求概率p = 10/28 ≈ 0.3571

（2）满足条件排列数 = C(2,5) + C(2,3) = 5!/(2!3!) + 3!/(2!1!) = 10 + 3 = 13

全排列 = C(2,8) = 8!/(2!6!) = (8!/6!)/2! = 8*7/2 = 28

∴所求概率p = 13/28 ≈ 0.4643

（3）（用排除法）

只取出黄球的排列数 = C(2,3) = 3!/(2!1!) = 3

全排列 = C(2,8) = 8!/(2!6!) = (8!/6!)/2! = 8*7/2 = 28

∴所求概率p = (28-3)/28 ≈ 0.8929