Answer :
To determine the probability that both dice will show a 3 when tossed, we will follow a structured approach.
1. Understand the Single Die Roll:
- A standard die has 6 faces, numbered from 1 to 6.
- Each face has an equal chance of appearing when the die is rolled.
- Therefore, the probability of rolling any specific number (such as a 3) on one die is:
[tex]\[ P(\text{rolling a 3 on one die}) = \frac{1}{6} \][/tex]
2. Analyze Two Independent Dice Rolls:
- When two dice are rolled, the outcome of one die does not affect the outcome of the other. The events are independent.
- We want to find the probability that both dice will show a 3 simultaneously.
3. Calculate the Combined Probability:
- Since each die roll is independent, we multiply the probabilities of each event occurring:
[tex]\[ P(\text{both dice showing a 3}) = P(\text{rolling a 3 on one die}) \times P(\text{rolling a 3 on the other die}) \][/tex]
Substituting the known probability of rolling a 3 on one die:
[tex]\[ P(\text{both dice showing a 3}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \][/tex]
Thus, the probability that both dice will show a 3 when rolled is:
[tex]\[ \frac{1}{36} \][/tex]
So, the correct choice is:
[tex]\[ \boxed{\frac{1}{36}} \][/tex]
1. Understand the Single Die Roll:
- A standard die has 6 faces, numbered from 1 to 6.
- Each face has an equal chance of appearing when the die is rolled.
- Therefore, the probability of rolling any specific number (such as a 3) on one die is:
[tex]\[ P(\text{rolling a 3 on one die}) = \frac{1}{6} \][/tex]
2. Analyze Two Independent Dice Rolls:
- When two dice are rolled, the outcome of one die does not affect the outcome of the other. The events are independent.
- We want to find the probability that both dice will show a 3 simultaneously.
3. Calculate the Combined Probability:
- Since each die roll is independent, we multiply the probabilities of each event occurring:
[tex]\[ P(\text{both dice showing a 3}) = P(\text{rolling a 3 on one die}) \times P(\text{rolling a 3 on the other die}) \][/tex]
Substituting the known probability of rolling a 3 on one die:
[tex]\[ P(\text{both dice showing a 3}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \][/tex]
Thus, the probability that both dice will show a 3 when rolled is:
[tex]\[ \frac{1}{36} \][/tex]
So, the correct choice is:
[tex]\[ \boxed{\frac{1}{36}} \][/tex]
