A person throws two fair dice. He wins Rs. 15 for throwing a doublet
( same numbers on the two dice), wins Rs. 12 when the throw results
in the sum of 9 , and loses Rs. 6 for any other outcome on the throw.
Then the expected gain / loss (in Rs.) of the person is :
gain
loss
loss
2 gain
Prob. of getting a doublet =1/6
Prob. of getting a sum of 9=1/9
Prob. of getting other outcomes=13/18
Now according to the ques.
After getting a doublet money gained by him=15×1/6 =5/2
After getting a sum of 9 money gained by him=1/9×12 =4/3
When there is any other outcome,he looses money=13/18×6 =13/3
So the complete loss or gain
=5/2 + 4/3 - 13/3= -1/2
This implies his expected result is loss of money and he looses 1/2rs .
Option 1
Option 2) 1/4 loss
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When 2 dice are thrown , Sample space would be
Now, the expected gain or loss = both + Sum (9) - other
So, there is loss of
Option 1)
Option 2)
Option 3)
Option 4)
2 gain