A student is taking a tough course in a weird school with no mercy. The student
ID: 3203207 • Letter: A
Question
A student is taking a tough course in a weird school with no mercy. The student gets an A with probability 0.1. a B with probability 0.4. and a grade C or lower with probability 0.5. The student passes the course only if he/she gets an A. The student does not take the course again if he/she passes it. A grade of B means that the student should repeat the course. A grade of C or lower means that the student fails the course, in which case he/she is not allowed to take the course again. Assume that each time the student takes the course is an independent trial. Find the probability that the student eventually fails the course. Find the probability that the student eventually passes the course. Consider now two students who start to take the course at the same semester. Suppose that their grades are independent of one another. Calculate the probability that the students pass the course in the same semester. E.g., they may both pass in the first semester they start, or they may both fail in the first semester, and pass in the second, and so on...Explanation / Answer
a)probabilty that he fails P(F) =P(he got a C+he got a B and then got a C+Got a B and then B and Then C+......)
=0.5+0.4*0.5+0.4*0.4*0.5+.... =0.5 +(0.4*0.5/(1-0.4)) =0.5+0.333=0.833
b) probabilty that he passes =P(S) =P(he got a A+he got a B and then got a A+Got a B and then B and Then A+......)
=0.1+0.4*0.1+0.4*0.4*0.1+0.4*0.4*0.4*0.1+...
=0.1+(0.4*0.1/(1-0.4)) =0.1+0.0667 =0.1667
this can be solved also by P(S) =1-P(F) =1-0.8333 =0.1667
c) probabilty that they passess together =P(they both got A +they both got B and they both got A after +...)
=0.1*0.1 +0.4*0.4*0.1*0.1+0.4*0.4*0.4*0.4*0.1*0.1+....
=0.01+(0.4*0.4*0.1*0.1/(1-0.4*0.4)) =0.01+0.0019 =0.0119
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