Question

What is the probability of getting at least one six in a single throw of three unbiased dice?
1. \(91\over 216\)
2. \(5\over 36\)
3. \(1\over 216\)
4. \(1\over 36\)

Answer 1

Correct Answer - Option 1 : \(91\over 216\)

Concept:

• The number of ways for selecting r from a group of n (n > r) = nCr 

• The probability of any event to occur = \(\rm \text{The required number of cases}\over\text{Total number of cases possible}\)

Calculation:

The total number of cases = 6 × 6 × 6 = 216

The number of ways no six appears = 5 × 5 × 5 = 125

The number of ways of at least one six = 216 - 125 = 91

∴ The required favorable probability = \(\boldsymbol{91\over 216}\)