Question

During a game, a one rupee coin is tossed thrice and obtained outcome is noted. If Haneef gets the same outcomes on the three coins i.e., either heads or tails, he will win the game, otherwise will be defeated. Find the probability of losing the game by Haneef.

Answer 1

When a coin of one rupee is tossed three times, the all possible outcomes are given as :

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Total number of all possible outcomes = 8.

Let the probability of getting same outcomes be (A).

The favourable outcomes of occurring same outcomes are HHH, TTT.

∴ The number of favourable outcomes = 2

∴ The probability that Haneef will win the game
P(A) = \(\frac { 2 }{ 8 }\) = \(\frac { 1 }{ 4 }\)

Let the probability of not winning the game be P(\(\overline { A }\))

∴ P(\(\overline { A }\)) = 1 – P(A)

P(\(\overline { A }\)) = 1 – \(\frac { 1 }{ 4 }\) = \(\frac { 3 }{ 4 }\)

Hence, the probability that Haneef will loss the game = \(\frac { 3 }{ 4 }\)