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.
Step-by-Step Solution
Key Concept: Sample space $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$ (8 outcomes). Winning outcomes: $HHH, TTT$ (2 outcomes). Losing outcomes: 6.
Stepwise Solution:
Total outcomes $N(S) = 2^3 = 8$. [1.0 Mark]
Winning outcomes $= \{HHH, TTT\}$ (2 outcomes). [1.0 Mark]
Losing outcomes $= 8 - 2 = 6$ outcomes.
$P(\text{Hanif loses}) = \dfrac{6}{8} = \dfrac{3}{4} = 0.75$. [1.0 Mark]
Marking Scheme:
• Total sample space size $= 8$: 1.0 Mark
• Identifying 2 winning outcomes {HHH, TTT}: 1.0 Mark
• Calculating probability of losing $= 6/8 = 3/4$: 1.0 Mark
Correct Answer: