Probability
Aptitude

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Q.

A person starting with 64 rupees and making 6 bets, wins three times and loses three times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is:

 A.

a gain of Rs 27

 B.

a loss of Rs 37

 C.

neither gain nor a loss

 D.

a gain or a loss depending upon the order in which the wins and losses occur

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Solution:
Option(B) is correct

As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).

The overall resultant will remain same.

So final amount with the person will be (in all cases):

$=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)=$ Rs $27$

Hence the final result is: 

$64-27=37$:

A loss of Rs 37

Note: Thank you Rahul, for explaining the concept behind using 1.5 and 0.5 as a multiplier in the comments.


(9) Comment(s)


Ajay Dubey
 ()

suppose if a person has 1 if lose then .5 and if win then 1.5 (



Rahul
 ()

Suppose you have Rs 64 and you win , you get Rs $64 + 32$ (Half of 64) Which is equal to multiplying $64 \times 1.5$

If you loose you loose Rs 32 which is half of Rs 64 which is equal to $65 \times 0.5$

So to solve the problem 64 is multiplied 03 times by 1.5 and 03 times by 0.5 . This is because there are 06 bets and 03 times you win and 03 times you loose.



Rahul
 ()

As mentioned in the question each bet is half the money remaining on the table. So that clearly says that if you will you get you half the money reamining on the table and if you loose you have to pay half the money remaining.

That is why it is multiplied by 1.5 when you win and multiply by 0.5 when you loose.



Jayanth
 ()

I think we can conclude the answer B by the question itself as below:

"If each wager is for half the money remaining at the time of the bet, then the final result is" any advice?



PRATYUSH ANAND
 ()

Hi,

1.5 they took because gain is 50% .

suppose you have Rs 10 and 50% gain . Then answer will be Rs $10\left(1+ \dfrac{50}{100}\right)$ or Rs $10 \times 1.5$.



Koinee
 ()

What if the amount changes,??


Rakesh
 ()

Then final answer changes.

I believe numbers are only to help you grasp the concept. If you get the fundamental point behind the problem, numbers don't matter.


Zahra
 ()

at initial step why the amount of 1.5 is multiply for the win , and why 0.5 for loss? whats the logic behind it?



Ananya
 ()

As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).

How did you take that 1.5 and 0.5 ? please explain