Multiple choice

Counters numbered $1,2,3$ are placed in a bag and one is drawn at random and replaced. The operation is being repeated three times. The probabolity of obtaining a total of $6$ is ?

  1. $\dfrac {7}{9}$
  2. $\dfrac {6}{27}$
  3. $\dfrac {7}{27}$
  4. $\dfrac {5}{27}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total outcomes = 3 * 3 * 3 = 27. Favorable outcomes for sum 6: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1), (2,2,2). There are 7 such outcomes. Probability = 7 / 27.

AI explanation

Since a counter is drawn and replaced three times, the total number of possible outcomes is 3^3, which equals 27. To obtain a total of 6, the possible combinations of numbers on the three draws are (1, 2, 3), (2, 2, 2), and (1, 1, 4). The combination (1, 1, 4) is impossible since the maximum number is 3. The combination (1, 2, 3) can be arranged in 3 factorial ways, which is 6, while (2, 2, 2) has only 1 arrangement, giving a total of 7 favorable outcomes. The required probability is 7 divided by 27.

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