Verified Solution • 2025–26 Session moderate

QJEEM19Ma4833: JEE Main 2019 Mathematics - Class 12 JEEM19Ma4833 Solution: In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a …

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

Multiple Choice Options

  • A 4003{{400} \over 3} loss
  • B 0
  • C 4009{{400} \over 9} loss
  • D 4003{{400} \over 3} gain

Step-by-Step Verified Solution

Expected Gain/Loss =

= w ×\times 100 + Lw( −- 50 + 100)

       + L2w ( −- 50 −- 50 + 100) + L3( −- 150)

= 13×100+23.13(50)+(23)2(13)(0){1 \over 3} \times 100 + {2 \over 3}.{1 \over 3}\left( {50} \right) + {\left( {{2 \over 3}} \right)^2}\left( {{1 \over 3}} \right)\left( 0 \right)

         +(23)3(−150)=0+ {\left( {{2 \over 3}} \right)^3}\left( { - 150} \right) = 0

here w denotes probability that outcome 5 or 6 (w = 26=13{2 \over 6} = {1 \over 3} )

here L denotes probability that outcome

1,2,3,4 (L = 46{4 \over 6} = 23{2 \over 3} )

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