Question

what is the probability of rolling an even number first and an odd number second?
1/9
1/6
1/4
1/2

Explanation:

Step1: Calculate probability of first - roll being even

There are 6 possible outcomes when rolling a die (1, 2, 3, 4, 5, 6), and 3 even numbers (2, 4, 6). So the probability of rolling an even number on the first roll, $P(A)=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability of second - roll being odd

There are 3 odd numbers (1, 3, 5) out of 6 possible outcomes. So the probability of rolling an odd number on the second roll, $P(B)=\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the two rolls of the die are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. Substitute $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{2}$ into the formula: $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$