Multiple choice

A six-faced fair dice is rolled five times. The probability (in %) of obtaining 'ONE' at least four times is

  1. 33.3

  2. 3.33

  3. 0.33

  4. 0.0033
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C Correct answer
Explanation

Probability of getting 'ONE' in one roll is 1/6. For 5 rolls, getting 'ONE' at least 4 times follows binomial distribution: P(X=4) + P(X=5). P(X=4) = 5C4 * (1/6)^4 * (5/6)^1 = 5 * (1/1296) * (5/6) = 25/7776. P(X=5) = 5C5 * (1/6)^5 = 1/7776. Total = 26/7776 approx 0.00334. As a percentage, this is 0.334%.

AI explanation

Using the binomial distribution formula, the probability of getting exactly four ones is 5C4 times (1/6)^4 times (5/6)^1, and the probability of getting exactly five ones is 5C5 times (1/6)^5. Adding these gives (25 + 1) divided by 7776, which equals 26/7776 or 1/299. Multiplying by 100 to convert to a percentage gives 0.33 percent.

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