Two urns contain coloured balls: Urn-I has 4 red and 2 white balls; Urn-II has 2 red and 4 white balls. One ball is drawn at random from Urn-I. If it is red, it is placed in Urn-II; if it is white, it is returned to Urn-I along with one extra white ball taken from Urn-II. Next, one ball is

Question

Two urns contain coloured balls: Urn-I has 4 red and 2 white balls; Urn-II has 2 red and 4 white balls. One ball is drawn at random from Urn-I. If it is red, it is placed in Urn-II; if it is white, it is returned to Urn-I along with one extra white ball taken from Urn-II. Next, one ball is drawn at random from Urn-II. If it is red, it is returned to Urn-II along with one extra red ball taken from Urn-I; if it is white, it is placed in Urn-I. After this pair of operations, it is observed that either the number of white balls in Urn-I is the same as initially, OR the number of red balls in Urn-I is the same as initially. Let p be the probability that the number of red balls in Urn-I remained the same as initially. Find the value of 17p.

Accepted Answer

7. There are four equiprobable-structured paths. In Path A (Red then Red from Urn-II) Urn-I ends with 2R 2W — white count preserved. In Path D (White then White from Urn-II) Urn-I ends with 4R 4W — red count preserved. These are the only two paths satisfying the given condition, so the conditional probability p of red being unchanged equals P(Path D) / (P(Path A) + P(Path D)).

Solution

Related JEE Main Physics questions