An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that (i) all will bear ‘X’ mark. (ii) not more than 2 will bear ‘Y’ mark. (iii) at least one ball will bear ‘Y’ mark (iv) the number of balls with ‘X’ mark and ‘Y’ mark will be equal.

An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the

1.	An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that (i) all will bear ‘X’ mark. (ii) not more than 2 will bear ‘Y’ mark. (iii) at least one ball will bear ‘Y’ mark (iv) the number of balls with ‘X’ mark and ‘Y’ mark will be equal.
Answer» An urn contains 25 balls of which 10 balls bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that (i) all will bear ‘X’ mark. (ii) not more than 2 will bear ‘Y’ mark. (iii) at least one ball will bear ‘Y’ mark (iv) the number of balls with ‘X’ mark and ‘Y’ mark will be equal.