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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

In a dice game, a player pays a stake of Re1 for each throw of a die.She receives Rs 5 if the die shows a 3,Rs 2 if the die shows a 1 or 6,and nothing otherwise.What is the player's expected profit per throw over a long series of throws?

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A)
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  • The possible outcum of throwof dice are\({1\;,2\;,3\;,4\;,5\;,6\;}\) each having the probability\(\Large\frac{1}{6}\)
  • He pays a stake of Re1
  • He define X to be the part of profit he get for each event of the game
  • Expected profit=\(\Large\sum_{i=1}^{6} x_ip_i\)
\(E(x)=\Large1\times\;\frac{1}{6}\;+-1\times\;\frac{1}{6}\;+4\times\;\frac{1}{6}\;+-1\times\;\frac{1}{6}\;+-1\times\;\frac{1}{6}\;+1\times\;\frac{1}{6}\)
=\(\Large\frac{3}{6}\)
=\(0.05\)

 

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