Question

additional example #3
two dice are rolled. what is the probability of getting two odd numbers on
two dice?
possible answers:
\\(\frac{2}{3}\\)
\\(\frac{1}{8}\\)
\\(\frac{1}{2}\\)
\\(\frac{1}{6}\\)
\\(\frac{1}{4}\\)

Explanation:

Step1: Determine probability for one die

A die has 6 faces: 1,2,3,4,5,6. Odd numbers are 1,3,5 (3 odd numbers). So probability of odd on one die: $\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability for two dice

Since the rolls are independent, multiply the probabilities. Probability of two odds: $\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$ (corresponding to the option with $\frac{1}{4}$)