Question

Two fair dice with faces numbered 1 to 6 are rolled together. Find the probability that both dice show odd numbers. (Give your answer rounded off to 2 decimal places.)

Hint:

When two independent events must occur together, multiply their probabilities: here \(\tfrac{3}{6}\times\tfrac{3}{6}=\tfrac{1}{4}\). Counting explicitly (\(9\) out of \(36\)) is a good cross-check.

Answer 1

Step 1: Define the sample space.
Each die has 6 equally likely outcomes. For two independent dice, total outcomes
\[ N = 6 \times 6 = 36. \] 

Step 2: Characterize the favourable outcomes.
Odd faces on a die are \(\{1,3,5\}\) \(\Rightarrow\) count \(=3\) per die.
Because the dice are independent, the number of ordered pairs with both odd is
\[ N_{\text{fav}} = 3 \times 3 = 9 \] (the pairs are \((1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\)). 

Step 3: Compute the probability and round.
\[ P(\text{odd on both})=\frac{N_{\text{fav}}}{N}=\frac{9}{36}=\frac{1}{4}=0.25. \] Rounding to two decimals leaves \(0.25\) unchanged.
\[\boxed{0.25}\]