题目
A portfolio manager annually outperforms her benchmark 60% of the time. Assuming independent annual trials, what is the probability that she will outperform her benchmark four or more times over the next five years?
选项
A.0.26
B.0.34
C.0.48
答案
B
解析
B is correct. To calculate the probability of 4 years of outperformance, use the formula:「huixue_img/importSubject/1564548697692442624.png」
Using this formula to calculate the probability in 4 of 5 years, n = 5, x = 4 and p = 0.60.Therefore,「huixue_img/importSubject/1564548697759551488.png」The probability of outperforming 4 or more times is p(4) + p(5) = 0.2592 + 0.0778 = 0.3370 B正确。 要计算4年的均是优越表现的概率，可以使用以下公式: P(x)=P(X=x)=[n!/(n-x)!x!](p^x)[(1-p)^(n-x)] 用这个公式计算5年内4次优越的概率，n = 5, x = 4, p = 0.60。 因此, P(4)= [5!/(5-4)!4!](0.6^4)[(1-0.6)^(5-4)]=[120/24](0.1296)(0.40)=0.2592 P(5)= [5!/(5-5)!5!](0.6^5)[(1-0.6)^(5-5)]=[120/120](0.0778)(1)=0.0778 超过4次或4次以上的概率是p(4)＋p(5) = 0.2592＋ 0.0778 = 0.3370 补充计算器按键步骤： 以：P(4)= [5!/(5-4)!4!](0.6^4)[(1-0.6)^(5-4)]=[120/24](0.1296)(0.40)=0.2592 为例 每个部分依次按（其中“ ”表示两个按键的连接并不是“加号”）： 1.5!/(5-4)!4!]：“5” “2ND” “ ” “4” “=”得出5 2.(0.6^4)：“0.6” “yx” “4”得出0.12960 3.[(1-0.6)^(5-4)]：“1” “-“ ”0.6” “=” “yx” “1”=0.4 将以上3个部分相乘5x0.12960x0.4=0.25920