A coin is tossed 3 times. List outcomes and find probability of (i) all heads (ii) at least two heads.
(i) \(\dfrac{1}{8}\), (ii) \(\dfrac{1}{2}\)
Step 1: Total outcomes when a coin is tossed 3 times
Each coin toss has 2 possible outcomes: Head (H) or Tail (T).
So, for 3 tosses: total outcomes = \(2^3 = 8\).
List of all outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Step 2: Probability of all heads (i)
From the list, only one outcome is all heads: HHH.
So, favourable outcomes = 1.
Total outcomes = 8.
Therefore, Probability = \( \dfrac{1}{8} \).
Step 3: Probability of at least two heads (ii)
"At least two heads" means the outcome should have either 2 heads or 3 heads.
Total favourable outcomes = 3 + 1 = 4.
Total outcomes = 8.
Therefore, Probability = \( \dfrac{4}{8} = \dfrac{1}{2} \).