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 headds in tossing a coin 3 times . Then, X can take value `0,1,2,3`.
Again, let `y = ₹ 2x`. Then, Y can taje the values ₹ 0, ₹ 2, ₹4, and ₹ 6
`:. P(y=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`