Final answer:
The probability of choosing a 5 and then a 6 when rolling a fair, six-sided die twice is 1/36.
Step-by-step explanation:
The probability of choosing a 5 and then a 6 when rolling a fair, six-sided die twice is determined by multiplying the probability of each individual event. The probability of rolling a 5 (P(5)) is ⅓ (1 out of 6), and the probability of rolling a 6 afterwards (P(6)) is also ⅓.
We multiply the two probabilities to get the combined probability of both events occurring in sequence:
P(5 and then 6) = P(5) × P(6) = ⅓ × ⅓ = ⅓² = ⅓×⅓ = 1/36
Therefore, the probability of rolling a 5 followed by a 6 is 1/36.