Question

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 1

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 \(\frac{^6C_3}{26} = \frac{5}{16}\).