A game consists of tossing a one rupee coin 3 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.

To find the probability that Hanif will lose the game, we first need to determine the total possible outcomes when tossing a coin three times.

Total Outcomes

Each toss of the coin has 2 possible results: heads (H) or tails (T). Therefore, for three tosses, the total number of outcomes can be calculated as:

• 2 (for the first toss) × 2 (for the second toss) × 2 (for the third toss) = 2³ = 8

Winning Outcomes

Hanif wins if all tosses are the same. The winning outcomes are:

• HHH (three heads)
• TTT (three tails)

Thus, there are 2 winning outcomes.

Losing Outcomes

To find the losing outcomes, we subtract the winning outcomes from the total outcomes:

• Total outcomes: 8
• Winning outcomes: 2
• Losing outcomes: 8 - 2 = 6

Calculating Probability

The probability that Hanif will lose the game is the number of losing outcomes divided by the total outcomes:

Probability of losing = Number of losing outcomes / Total outcomes

Probability of losing = 6 / 8 = 3 / 4

Final Result

Therefore, the probability that Hanif will lose the game is 3/4 or 75%.