Q.N. 9) From past experience, a statistics professor knows that 85% of his stude
ID: 3429774 • Letter: Q
Question
Q.N. 9) From past experience, a statistics professor knows that 85% of his students who do the test review problems pass the test, and of those who do not do the review problems, 90% fail. Before he starts to grade the latest test, he believes that 95% of his students did the review problems. The first randomly selected test he grades receives a failing grade. Find the conditional probability that the student did the review. Q.N. 10) If A and B are independent events, prove that A^c and B^c are independent. Note that A^c and B^c are the compliments of A and B respectively.Explanation / Answer
9.
let A be the event of the student failing the test.
let B be the event of the student did the review.
=>
P(AnB) = 0.95*0.15 =0.1425
P(B) = 0.95*0.15 + 0.05* 0.90 = 0.1875
=>
the required probability = P(A|B) = 0.1425/0.1875 = 0.76
10)
P(AnB) = P(A)P(B)
P(A' n B') = 1-P(AuB) = 1- [P(A) + P(B) -P(AnB)]
= 1-P(A)-P(B) + P(AnB)
= 1-P(A)-P(B) + P(A)P(B)
= (1-P(A))(1-P(B))
= P(A')P(B')
=>
P(A'nB') = P(A')P(B')
=>
A', B' are independent events
thus proved
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.