you roll a 6 - sided die two times. what is the probability of rolling an odd number and then rolling an…

Explanation:

Step1: Find probability of odd - roll

On a 6 - sided die, odd numbers are 1, 3, 5. So the probability of rolling an odd number on the first roll, $P(O_1)=\frac{3}{6}=\frac{1}{2}$.

Step2: Find probability of even - roll

On a 6 - sided die, even numbers are 2, 4, 6. So the probability of rolling an even number on the second roll, $P(E_2)=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the two rolls are independent events, the probability of rolling an odd number first and then an even number is $P = P(O_1)\times P(E_2)$. Substituting the values, we get $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step4: Convert to percentage

To convert $\frac{1}{4}$ to a percentage, we multiply by 100. So $P=\frac{1}{4}\times100 = 25%$.

Answer:

25%