Question

Purse $I$ contains a one rupee coin and nine 50 paise coins and purse $II$ contains ten 50 paise coins. 9 coins are transferred from purse $I$ to purse $II$ and again from purse $II$ to purse $I$ randomly. The probability of finding one rupee coin in the purse $I$ after these transfers is

• A. $\frac{1}{10}$
• B. $\frac{9}{19}$
• C. $\frac{10}{19}$
• D. $\frac{9}{10}$

Answer 1

Answer: (C)

$\frac{10}{19}$

The one rupee coin can be found if:
(i) only 50p coins are transferred to and fro
(ii) the one rupee coin is transferred and again brought back
Hence, probability $=(\frac{{}_9^{9}C}{{}_9^{10}C}\ast 1)+(\frac{{}_8^{9}C{\ast }_1^{1}C}{{}_9^{10}C}\ast \frac{{}_8^{18}C{\ast }_1^{1}C}{{}_9^{19}C})=\frac{1}{10}+\frac{81}{190}=\frac{10}{19}$