A bowl contains (m) white marbles and (n) red marbles. A marble is taken randomly from the

Question:

A bowl contains \(m\) white marbles and \(n\) red marbles. A marble is taken randomly from the bowl and returned to the bowl together with \(r\) marbles of the same color. This procedure continues to infinity.

(1) What is the probability that the second marble taken is red?

(2) What is the probability that the first marble taken is red on condition that the second marble taken is red? (This is a variant of Pólya's urn problem.)

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Manu Singh

In the 4 years of my teaching career, I have a really amazing experiences while dealing with student problems that is conceptual doubts and his/her personal problems and I really believe that teacher is not person who just used to teach concepts of book rather he/she is the person who also teach about life. In every new session, I used to teach new students with their new mental level and new problems and this thing makes me feel challenging and l really love facing these challenges with full of excitement and joy. Sometimes I also feel under pressure when high school final exam are on our head but I handle these kind of situation very gently because of my corporate experience. If I talk about why I do this job then I really wanna say that teaching taught me a lot things like strong conceptual knowledge of subjects like physics and mathematics and now it is helping me in my graduation, strong listening and observation skill and I feel that to be good teacher , one should be a great listener and observer to understand the problems of students accurately and to give a proper answer because sometimes students are not in the situation to share their problems with teacher so here teacher need to be keen observer to understand the problem of their students. It also taught me to work under pressure and to make environments enjoyable and full of fun etc. Teaching also helped me to increase my thinking power whenever students ask their doubts, sometimes fictional then i really need to push the muscles of my brain and this excites me. Since I am an mechanical engineer so I teach my students with lots of practical examples and I also explain them what is the future use of their current study because I feel this'll create curiosity in their mind about subject and it is very important for students.

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