Multiple choice

Three faces of a fair dice are yellow, two faces red and one blue. The die is tossed 3-times. The probability that the colours yellow, red and blue appear in the first, second and the third tosses respectively is .............

  1. $1/36$
  2. $1/216$
  3. $1/72$
  4. $1/108$
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A Correct answer
Explanation

Probability of yellow = 3/6 = 1/2. Probability of red = 2/6 = 1/3. Probability of blue = 1/6. The probability of the sequence (yellow, red, blue) is (1/2) * (1/3) * (1/6) = 1/36.

AI explanation

For a custom die, the probability of each outcome is the number of corresponding faces divided by the total number of 6 faces. The individual probabilities for yellow, red and blue are 3/6, 2/6 and 1/6 respectively. Using the multiplication theorem for independent events, the probability of getting yellow, red and blue in three successive tosses is (3/6) multiplied by (2/6) multiplied by (1/6), which equals 6/216 or 1/36.

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