probability?

[匿名]

2015-11-16 11:20 am

From a survey to assess the attitude of students in their study, 0.8 of them are highly
motivated, 0.9 are hard working, and only 0.05 are neither highly motivated nor hard
working.
(a) Calculate the probability that a randomly selected student is both highly motivated
and hard working.
(b) Given that the student is hard working, what is the probability that this student is
not highly motivated?

回答 (1)

YA HOO！知識＋管理員

2015-11-16 12:14 pm

✔ 最佳答案

P(E∪F) = P(E) + P(F) - P(E∩F)
P(E∩F) = P(E) P(F|E) = P(F) P(E|F)

(a)
P(highly motivated) = 0.8　　P(hard working) = 0.9

Let P(highly motivated or hard working) = x
P(highly motivated or hard working) + P(neither highly motivated nor hard working) = 1
P(highly motivated or hard working) = 1 - 0.05 = 0.95
P(highly motivated) + P(hard working) - P(both highly motivated and hard working) = 0.95
P(both highly motivated and hard working) = 0.9 + 0.8 - 0.95 = 0.75

(b)
P(not highly motivated and hard working)
= P(hard working) - P(highly motivated and hard working)
= 0.9 - 0.75
= 0.15

P(not highly motivated | hard working) P(hard working) = P(not highly motivated and hard working)
P(not highly motivated | hard working) = 0.15 / 0.9 = 1/6

👍 0 👎 0