Two dice are thrown. Find the probability of getting (i) the same number on both, (ii) different numbers.
(i) \(\dfrac{1}{6}\); (ii) \(\dfrac{5}{6}\)
Step 1: Total outcomes when 2 dice are thrown
Each die has 6 faces numbered from 1 to 6. When two dice are thrown together, the number of total outcomes = \(6 \times 6 = 36\).
Step 2: Case (i) – Getting the same number on both dice
Same number means both dice show equal numbers (like (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)). So, there are 6 such outcomes.
Probability = \(\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}} = \dfrac{6}{36} = \dfrac{1}{6}\).
Step 3: Case (ii) – Getting different numbers on both dice
If they are not the same, then they must be different. Total outcomes = 36, outcomes with same number = 6. So, outcomes with different numbers = \(36 - 6 = 30\).
Probability = \(\dfrac{30}{36} = \dfrac{5}{6}\).
Final Answer:
(i) Probability of same number = \(\dfrac{1}{6}\)
(ii) Probability of different numbers = \(\dfrac{5}{6}\)