Project ForgeEngineering Mathematics
Calculus
GATE 2018
Hard
A six-faced fair dice is rolled five times. The probability (in %) of obtaining "ONE" at least four times is
- A33.3
- B3.33
- 0.33
- D0.0033
Explanation
P(≥4 of 5) = P(exactly 4) + P(exactly 5), with p=1/6, n=5. P(4) = C(5,4)(1/6)⁴(5/6) = 5×5/7776 = 25/7776 ≈ 0.003215. P(5) = (1/6)⁵ = 1/7776 ≈ 0.0001286. Sum ≈ 0.003344 = 0.33%.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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