Question
Jill has two dimes she is going to use to perform a probability experiment. What is the theoretical probability that at least one of the two coins will turn up heads?
50%
75%
25%
0%
50%
75%
25%
0%
Answers
GPT-4o mini
To find the theoretical probability that at least one of the two coins (two dimes) will turn up heads, we can use a simple probability method.
First, let's outline the possible outcomes when tossing two coins:
1. HH (both heads)
2. HT (one head, one tail)
3. TH (one tail, one head)
4. TT (both tails)
Out of these four possible outcomes, the following outcomes include at least one head:
1. HH
2. HT
3. TH
That gives us a total of 3 successful outcomes that include at least one head.
Now, let's calculate the probability:
- Total outcomes = 4
- Successful outcomes (at least one head) = 3
The theoretical probability is calculated as:
\[
P(\text{at least one head}) = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{3}{4} = 0.75 \text{ or } 75\%
\]
Therefore, the theoretical probability that at least one of the two coins will turn up heads is **75%**.
First, let's outline the possible outcomes when tossing two coins:
1. HH (both heads)
2. HT (one head, one tail)
3. TH (one tail, one head)
4. TT (both tails)
Out of these four possible outcomes, the following outcomes include at least one head:
1. HH
2. HT
3. TH
That gives us a total of 3 successful outcomes that include at least one head.
Now, let's calculate the probability:
- Total outcomes = 4
- Successful outcomes (at least one head) = 3
The theoretical probability is calculated as:
\[
P(\text{at least one head}) = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{3}{4} = 0.75 \text{ or } 75\%
\]
Therefore, the theoretical probability that at least one of the two coins will turn up heads is **75%**.