Multiple choice

An unbiased cubic die marked with $1,2,2,3,3,3$ is rolled $3$ times. The probability of getting a total score of $4$ or $ 6$ is

  1. $\dfrac { 16 }{ 216 } $
  2. $\dfrac { 50 }{ 216 } $
  3. $\dfrac { 60 }{ 216 } $

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

The die has one face marked 1, two faces marked 2, and three faces marked 3. To get a total of 4, the possible outcomes are (1, 1, 2), (1, 2, 1), and (2, 1, 1). The probability for each of these three permutations is (1/6) times (2/6) times (1/6), which equals 2/216, so the total probability for a sum of 4 is 6/216. To get a total of 6, the possibilities are the permutations of (1, 2, 3), which is 6 arrangements each with a probability of (1/6) times (2/6) times (3/6) equaling 6/216 (for a sum of 36/216), and the permutations of (2, 2, 2), which is 1 arrangement with a probability of (2/6) times (2/6) times (2/6) equaling 8/216. Adding the probabilities for both totals, 6/216 + 36/216 + 8/216, gives 50/216.

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