In a game, a child will win Rs 5 if he gets all heads or all tails when three coins are tossed simultaneously and he will lose Rs 3 for all other cases. The expected amount to lose in the game is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 1
Three coins give 8 equally likely outcomes. All heads (HHH) or all tails (TTT) are 2 of them:
\( \displaystyle P(\text{win}) = \frac{2}{8} = \frac{1}{4},\quad P(\text{lose}) = \frac{3}{4} \)
Let X be the child’s gain in rupees: X = 5 or X = −3. The expected value is
\( \displaystyle E(X) = 5 \times \frac{1}{4} + (-3) \times \frac{3}{4} \)
\( \displaystyle = \frac{5 - 9}{4} = -1 \)
An expected gain of −Rs. 1 means an expected loss of Rs. 1.