ISRO-DEC2017-3

Question

 A bag contains $19$ red balls and $19$ black balls.Two balls are removed at a time repeatedly and discarded if they are of the same colour, but if they are different, black ball is discarded and red ball is returned to the bag ,The probability that this process will terminate with one red ball is 

• A. $1$
   
• B. $\dfrac{1}{21}$
   
• C. $0$
   
• D. $0.5$

Comments

refer this-> https://gateoverflow.in/182053/isro-dec2017-3

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Why (black,black,red) will not granted here?

if two black is chosen then single red will remain and

one red ,one black chosen then one red remain afterthat one black,red single red remain.

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@srestha the event(left with 1 red ball) will occur eventually that is why probability is 1

probability that an event will certainly occur, p=1 i.e. 100%

Answer 1

Lets consider the case 
RR
RB
BB
BR

The case BB never occurs as red balls are odd red only diminish when it is even number.
so we are left with three cases which result in only red remaining and hence whatever be the removal sequence we have red remain in the bag.

Answer is A.

Answer 2

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it will be 1,

black balls will  always get finished up, because it will either come with black(then both black balls are discarded) or it will come with red(only black ball will be discarded), now red balls will be only discarded in pairs(means always even no. of red balls are discarded), now since there are 19(odd) red balls, only 18 among them will be discarded.

final content of bag at second last trial will be either (red, black) or (red, red, red) and finally in last trial bag will left with one red ball only in both the cases,

hence, probability of above experiment is 1.

Answer 3

It Must Be Ans A