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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Probability

NDA 2025 · Mathematics · Probability

Three faces of a die are black, two faces are white and one face is...

Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the colours black, white and red appear in the first, second and third tosses respectively?

Options

  1. A1/361/36
  2. B1/61/6
  3. C7/367/36
  4. D5/365/36

Correct answer

A. 1/361/36

Step-by-step solution

Total number of faces on the die is 66.

Number of black faces is 33.
Probability of getting a black face in the first toss is P(B)=36=12P(B) = \dfrac{3}{6} = \dfrac{1}{2}.

Number of white faces is 22.
Probability of getting a white face in the second toss is P(W)=26=13P(W) = \dfrac{2}{6} = \dfrac{1}{3}.

Number of red faces is 11.
Probability of getting a red face in the third toss is P(R)=16P(R) = \dfrac{1}{6}.

Since the tosses are independent events, the required probability is the product of the individual probabilities.

Required probability =P(B)×P(W)×P(R)=12×13×16=136= P(B) \times P(W) \times P(R) = \dfrac{1}{2} \times \dfrac{1}{3} \times \dfrac{1}{6} = \dfrac{1}{36}.

Answer: 1/361/36
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