Question

If a 12-sided fair die is rolled twice, find the probability that both rolls have a result of 8.

(a) \(\frac{2}{19}\)

(b) \(\frac{3}{47}\)

(c) \(\frac{1}{64}\)

(d) \(\frac{2}{9}\)

This question was posed to me in an interview for internship.

I'd like to ask this question from Multiplication Theorem on Probability topic in division Discrete Probability of Discrete Mathematics

Answer 1

Right answer is (c) \(\frac{1}{64}\)

To explain: Each die roll is independent, that is, if the first die roll result is 8, it will not affect the probability of the second die roll resulting in 8. The probability of rolling one die is \(\frac{1}{8}\). Now, P (1st roll is 8 ∩ 2nd roll is 8). By using the rule of product: \(\frac{1}{8} * \frac{1}{8}\). Hence, the probability that both die rolls are 8 is \(\frac{1}{64}\).