In a game, a fair coin is tossed 6 times. Each time the coin comes up tails, A will pay Rs. 15 but if each time heads come up, A will pay nothing. Determine the probability that A will win Rs. 45 by playing the game?(a) \(\frac{5}{16}\)(b) \(\frac{4}{31}\)(c) \(\frac{3}{7}\)(d) \(\frac{12}{65}\)I have been asked this question in an online quiz.This intriguing question comes from Counting in portion Counting of Discrete Mathematics

In a game, a fair coin is tossed 6 times. Each time the coin comes up

1.	In a game, a fair coin is tossed 6 times. Each time the coin comes up tails, A will pay Rs. 15 but if each time heads come up, A will pay nothing. Determine the probability that A will win Rs. 45 by playing the game?(a) \(\frac{5}{16}\)(b) \(\frac{4}{31}\)(c) \(\frac{3}{7}\)(d) \(\frac{12}{65}\)I have been asked this question in an online quiz.This intriguing question comes from Counting in portion Counting of Discrete Mathematics
Answer» The correct option is (a) \(\frac{5}{16}\) Explanation: By using the binomial distribution, to calculate how LIKELY to win Rs. 45 (or equivalently, the likelihood the coin comes up tails 3 TIMES). The POSSIBLE outcomes of this game are to win Rs. 45. Therefore, the required probability is \(\frac{^6C_3}{26} = \frac{5}{16}\).

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