A person throws two fair dice. HE wins ₹ 15 for throwing a doublet (same numbers on the two dice), wins ₹ 12 when the throw results in the sum of 9, and losses ₹ 6 for any other outcome on the throw. Then, the expected gain/loss (in ₹) of the person is

Options

A. `(1)/(2)`gain
B. `(1)/(4)` loss
C. `(1)/(2)` loss
D. 2 gain

Answer

C

Explanation

It is given that a person wins
₹15 for throwing a doublet (1,1),(2,2),(3,3) (4,4), (5,5), (6,6) and win ₹ 12 when the throw results in sum of 9,i.e when (3,6), (4,5)
Also , loses ₹ for throwing any other outcome ,i.e when any of the rest 36-6 -4=26 outcomes occurs
Now, the expected gain/loss
`15xxP " (getting a doublet) " +12xxP " (getting sum 9) " -6xxP` (getting any of rest 26 outcome )
`(15xx6/(36))+(12xx4/(36))-(6xx(26)/(36))`
`5/2+4/3-(26)/6=(15+8-26)/6`
`(23-26)/6=-3/6=-1/2, " means loss of " ₹1/2`