Question

a single six - sided die is rolled twice. what is the probability of rolling an odd number on the first roll and an even number on the second roll? a. \\(\frac{1}{6}\\) b. \\(\frac{1}{30}\\) c. \\(\frac{1}{4}\\) d. \\(\frac{1}{12}\\)

Explanation:

Step1: Find P(odd on first roll)

Odd numbers on a die: 1,3,5. Total outcomes: 6.
$P(\text{odd}) = \frac{3}{6} = \frac{1}{2}$

Step2: Find P(even on second roll)

Even numbers on a die: 2,4,6. Total outcomes: 6.
$P(\text{even}) = \frac{3}{6} = \frac{1}{2}$

Step3: Multiply independent probabilities

Since rolls are independent, multiply the two probabilities.
$P(\text{odd then even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Answer:

C. $\frac{1}{4}$