Certainly! Let's go through the solution step-by-step to determine the probability of tossing heads and rolling a number less than 5.
1. Determine the Total Number of Possible Outcomes:
- When we toss a coin, there are 2 possible outcomes: Heads (H) or Tails (T).
- When we roll a 6-sided die, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.
- Thus, the total number of possible outcomes when combining these two events (tossing a coin and rolling a die) is [tex]\( 2 \times 6 = 12 \)[/tex].
2. Identify the Favorable Outcomes:
- We are interested in the outcomes where we get Heads (H) and a number less than 5 on the die.
- The numbers on the die less than 5 are: 1, 2, 3, 4.
- So, the favorable outcomes can be listed as: H1, H2, H3, and H4.
- Hence, there are 4 favorable outcomes.
3. Calculate the Probability:
- Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
- Therefore, the probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
- Plugging in our numbers, we get:
[tex]\[
\text{Probability} = \frac{4}{12} = \frac{1}{3}
\][/tex]
Therefore, the probability of tossing heads and rolling a number less than 5 is [tex]\( \frac{1}{3} \)[/tex].
So, the correct answer is:
B. [tex]\( \frac{1}{3} \)[/tex]
