There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
~$\frac{1}{2}$~
~$\frac{2}{3}$~
~$\frac{32}{35}$~
~$\frac{11}{12}$~
~$\frac{13}{14}$~
“至少有一本时尚杂志”的互斥事件是“3本全是体育杂志”
第一本是体育杂志的概率 4/8 第二本 3/7 第三本 2/6
故“3本全是体育杂志”的发生概率是 4/8*3/7*2/6=1/14
则其互斥事件发生的概率即为13/14
{at least one}={total}-{none}
total: 8*7*6 / 3! =56
none: 4*4*2 / 3! = 4
at least one = 56-4 = 52
probability = 52/56 = 13/14
1本是时尚杂志且2本是体育杂志的概率==C(1,4)*C(2,4)/C(3,8);2本是时尚杂志且1本是体育杂志的概率=C(2,4)*C(1,4)/C(3,8);3本是时尚杂志的概率=C(3,4)/C(3,8),三者相加=13/14
1. 共有56种情况,C(3,8),其中全是sports的有4种,C(3,4), at least有52种,52/56 = 13/14
2. (4*3*2 )/ (8*7*6)= 1/14, 1 - 1/14 = 13/14
直接算抽不到Fashion的概率,则(1/2)*(3/7)(1/3)=1/14。答案是13/14
to solve "at least one" combinations/probability questions with {at least one}={total}-{none}
{Total} = {Students} + {Employed} - {Both} + {Neither}
我们并不了解{Neither}的学生数量,缺少条件无法计算
抽到1f+抽到2f + 抽到 3f的概率相加