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A game consists of tossing a one rupee coin three times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.
  • a)
    1/4
  • b)
    1/2
  • c)
    3/4
  • d)
    5/8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A game consists of tossing a one rupee coin three times and noting its...
Probability of Losing the Game
To calculate the probability that Hanif will lose the game, we need to consider all the possible outcomes when tossing a one rupee coin three times.

Possible Outcomes
- When tossing a coin three times, there are a total of 2 x 2 x 2 = 8 possible outcomes.
- These outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Winning Outcomes
- Hanif wins the game if all tosses give the same result (three heads or three tails).
- The winning outcomes are HHH and TTT, which are 2 out of the 8 possible outcomes.

Probability of Winning
- The probability of winning the game is given by the number of winning outcomes divided by the total number of possible outcomes.
- Probability of winning = 2/8 = 1/4

Probability of Losing
- Since the probability of winning is 1/4, the probability of losing the game is the complement of winning.
- Probability of losing = 1 - 1/4 = 3/4
Therefore, the probability that Hanif will lose the game is 3/4.
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Community Answer
A game consists of tossing a one rupee coin three times and noting its...
We use the basic formula of favorable outcomes to solve the problem.
Total possible outcomes are = {HHH, TTT, HTH, HHT, THH, THT, TTH, HTT} = 8
Number of possible outcomes to get three heads or three tails is 2
The probability that Hanif will win the game = Number of possible outcomes/Total number of favourable outcomes
= 2/8
= 1/4
The probability that Hanif will lose the game is 1 - 1/4
= 3/4
The probability that Hanif will lose the game is 3/4.
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