Question

Allistair throws a biased six-sided dice. The probability of getting a 6 with this dice is 0.4. The other numbers are equally probable.

If he throws the dice 3 times, what is the probability that he gets 5, 3 and 2 in this order?
A. ≈0.291
B. ≈0.0578
C. ≈0.00173
D. ≈0.0127

Answer 1

The probability of rolling a 5, then a 3, and then a 2 with a biased six-sided dice where the probability of rolling a 6 is 0.4 is approximately 0.00173, corresponding to option C.

Step-by-step explanation:

The question asks for the probability of rolling a 5, then a 3, and then a 2 in that specific order with a biased six-sided dice. Given that the probability of rolling a 6 is 0.4, we can deduce that the remaining five sides have equal probabilities. Thus, the probability of rolling any number other than 6 is (1 - 0.4) / 5 = 0.12 for each number. When calculating the probability of independent events, we multiply the individual probabilities of each event occurring.

Therefore, the probability of rolling a 5, followed by a 3, and then a 2 is calculated as:

P(5) × P(3) × P(2) = 0.12 × 0.12 × 0.12 = 0.001728.

Rounding this result gives us a probability of approximately 0.00173, which matches option C.