In a game, 3 coins are tossed. A person is paid ₹150 if he gets all heads or all tails and he is supposed to pay ₹50 if he gets one head or two heads. The amount he can expect to win / lose on an average per game in ₹ is

Step-by-step solution

The expected value of the game is calculated using E = (x_i P(x_i)) where x_i represents the payout for each outcome and P(x_i) its probability. When tossing three coins, the sample space contains 2^3 = 8 equally likely outcomes. All heads or all tails occurs in 2 outcomes with probability 2 8 = 1 4 and yields ₹150. Exactly one or two heads occurs in the remaining 6 outcomes with probability 6 8 = 3 4 and costs ₹50. The expected value is: E = (150 1 4 ) + (-50 3 4 ) = 150 4 - 150 4 = 0 The expected win/loss amount