Question

A player tosses two fair coins. He wins $Rs.5/-$ if two heads occur, $Rs.$ $2/-$ if one head occurs and $Rs.$ $1/-$ if no head occurs. Then his expected gain is

• A. $Rs.\frac{8}{3}$
• B. $Rs.\frac{7}{3}$
• C. $Rs.2.5$
• D. $Rs.1.5$

Answer 1

The correct option is C $Rs.2.5$

Expected value$=\sum x\left(i\right)P\left(x\right(i\left)\right)$
Expected gain$=5\ast 1/4+2\ast 1/2+1\ast 1/4=2.5$