15. A game being offered in a casino consists of guessing the outcomes of two tosses of a fair coin. The gambler wins if she/he has correctly guessed at least one of the two tosses. To play a game, the gambler has to pay a fee of Rs. 80, and the winner gets a reward of Rs. 100 on winning the game (and nothing otherwise). Which of the following statements are correct? (a) In the first 10 minutes on a given day exactly three gamblers play the game, one after the other. The probability that the casino owner makes a profit in the first 10 minutes equals $1 / 4$. (b) One gambler plays the game three times. The probability that she wins exactly two of the three games is $27 / 64$. (c) Three friends go together and play the game with each playing once. The probability that all three win equals $27 / 64$. (d) If 1200 players play the game on a given day, the expected profit of the casino owner for the day equals Rs. 6000.
15. A game being offered in a casino consists of guessing the outcomes of two tosses of a fair coin. The gambler wins if she/he has correctly guessed at least one of the two tosses. To play a game, the gambler has to pay a fee of Rs. 80, and the winner gets a reward of Rs. 100 on winning the game (and nothing otherwise).\\
Which of the following statements are correct?\\
(a) In the first 10 minutes on a given day exactly three gamblers play the game, one after the other. The probability that the casino owner makes a profit in the first 10 minutes equals $1 / 4$.\\
(b) One gambler plays the game three times. The probability that she wins exactly two of the three games is $27 / 64$.\\
(c) Three friends go together and play the game with each playing once. The probability that all three win equals $27 / 64$.\\
(d) If 1200 players play the game on a given day, the expected profit of the casino owner for the day equals Rs. 6000.\\