Multiple choice

We roll a fair four-sided die. If the result is $1$ or $2$, we roll once more but otherwise, we stop. What is the probability that the sum total of our rolls is at least $4$?

  1. $\dfrac{1}{16}$
  2. $\dfrac{4}{16}$
  3. $\dfrac{7}{16}$
  4. $\dfrac{9}{16}$
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D Correct answer
Explanation

Possible outcomes: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3), (4). Total outcomes = 10. Outcomes with sum >= 4: (1,3), (1,4), (2,2), (2,3), (2,4), (3), (4). There are 7 favorable outcomes out of 16 equally likely paths in the tree diagram (1/4 * 1/4 for each branch). The probability is 9/16.

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