Question

you roll a 6-sided die two times.
what is the probability of rolling a 5 and then rolling a 2?
write your answer as a fraction or whole number.

Explanation:

Step1: Probability of rolling a 5

A 6 - sided die has 6 possible outcomes. The probability of rolling a 5 is the number of favorable outcomes (1, since there's one 5 on a die) divided by the total number of outcomes (6). So, $P(5)=\frac{1}{6}$.

Step2: Probability of rolling a 2

Similarly, the probability of rolling a 2 on a 6 - sided die is also the number of favorable outcomes (1) divided by the total number of outcomes (6). So, $P(2)=\frac{1}{6}$.

Step3: Probability of both events (rolling 5 then 2)

Since the two die rolls are independent events, the probability of both events happening is the product of their individual probabilities. So, $P(5\ then\ 2)=P(5)\times P(2)=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

$\frac{1}{36}$