A boy tosses faiir coin 3 times. If he gets Rs 2X for X heads, then his expected gain equals to Rs…..

Options

A. 1
B. `(3)/(2)`
C. 3
D. 4

Answer

C

Explanation

Let X be a random variable. That denotes the number of heads in tossing a coin 3 times. Then, X can take value 0,1,2,3.
Again let y=Rs. 2x. Then, Y can take the values
Rs. 0, Rs. 2, Rs 4 and Rs. 6
`therefore(Py=0)=P("getting 0 head")=(1)/(8)`
`P(y=2)=P("getting 1 head")=(3)/(8)`
`P(y=4)=P("getting 2 heads")=(3)/(8)`
`P(y=6)=P("getting 3 heads")=(1)/(8)`
Expected gain `=sumy_(i)p_(i)=0((1)/(8))+2((3)/(8))+4((1)/(8))+6((1)/(8))`
`=(6+12+6)/(8)=(24)/(8)=3`