To determine the probability of tossing heads and rolling a number less than 5, we need to follow these steps:
1. Understand the sample space:
- The sample space includes all possible outcomes when tossing a coin and rolling a number cube.
- For heads (H), the outcomes are H1, H2, H3, H4, H5, and H6.
- For tails (T), the outcomes are T1, T2, T3, T4, T5, and T6.
- Thus, the total number of outcomes is 12, which includes 6 outcomes for heads and 6 for tails.
2. Identify favorable outcomes:
- We want the outcomes where the coin shows heads and the number rolled is less than 5.
- These outcomes are H1, H2, H3, and H4.
3. Count the number of favorable outcomes:
- The number of favorable outcomes (tossing heads and rolling a number less than 5) is 4.
4. Calculate the probability:
- Probability is calculated as the number of favorable outcomes divided by the total number of outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\][/tex]
- Here, the number of favorable outcomes is 4, and the total number of outcomes is 12.
[tex]\[
\text{Probability} = \frac{4}{12} = \frac{1}{3}
\][/tex]
So, the probability of tossing heads and rolling a number less than 5 is approximately 0.3333, or [tex]\(\frac{1}{3}\)[/tex] when expressed as a fraction.
