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Byju's Answer

Standard XII

Physics

Projectile from a Height

A gambler rol...

Question

A gambler rolls two fair dice having the faces marked as $1, 2, 3, 4, 5, 6$ and stands to lose $R e . 1$ if he fails to throw a six; to win $R s . 2$ if he throws one six, and to win $R s . 5$ if he throws two sixes. Is the game fair?

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Solution

Total no. of possibilities on two dice $= 36$
No. of possibilities with $6$ on both dice $= 1$
No. of possibilities with $6$ on one dice $10$
No. of possibilities with $6$ on neither dice $= 25$
Amount of money:-
For winning $= (5 \times 1) + (2 \times 10)$
$= 25$
For lossing $= (25 \times 1)$
$= R s .25$
Both amount are same for winnning and lossing so the game is fair.

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A gambler rolls two fair dice having the faces marked as 1,2,3,4,5,6 and stands to lose Re.1 if he fails to throw a six; to win Rs. 2 if he throws one six, and to win Rs. 5 if he throws two sixes. Is the game fair?

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