Question

You toss a coin and roll a number cube. Find P (heads and an even number).


1

Answer 1

To find the probability \( P(\text{heads and an even number}) \) when tossing a coin and rolling a number cube (a standard six-sided die), we need to consider the possible outcomes for both the coin toss and the die roll.

1. **Coin Toss Outcomes**:
- Heads (H)
- Tails (T)

Therefore, there are 2 outcomes for the coin toss.

2. **Number Cube Outcomes**:
The numbers on a standard die are 1, 2, 3, 4, 5, and 6. The even numbers among these are 2, 4, and 6.

Therefore, there are 3 even outcomes when rolling a number cube.

3. **Calculating Total Outcomes**:
The total number of combined outcomes from both the coin toss and the die roll is:
\[
2 \text{ (coin outcomes)} \times 6 \text{ (die outcomes)} = 12 \text{ total outcomes.}
\]

4. **Favorable Outcomes**:
We are looking for the outcomes where we have heads (H) and an even number on the die. The possibilities are:
- (H, 2)
- (H, 4)
- (H, 6)

Thus, there are 3 favorable outcomes.

5. **Calculating Probability**:
The probability \( P(\text{heads and an even number}) \) is given by the ratio of favorable outcomes to the total outcomes:
\[
P(\text{heads and an even number}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{12} = \frac{1}{4}.
\]

So, the probability \( P(\text{heads and an even number}) \) is \( \frac{1}{4} \).