Answer :
To solve the problem of finding the probability that you flip "heads" on a coin and roll a number greater than 5 on a die, we need to break the problem down into steps.
1. Determine the probability of flipping "heads" on the coin:
- A standard coin has two sides, "heads" and "tails". Therefore, the probability of flipping "heads" is:
[tex]\[ P(\text{heads}) = \frac{1}{2} \][/tex]
2. Determine the probability of rolling a number greater than 5 on the die:
- A standard die has six sides, numbered 1 through 6.
- The numbers greater than 5 are just 6.
- There is only 1 favorable outcome (rolling a 6) out of 6 possible outcomes. Therefore, the probability of rolling a number greater than 5 is:
[tex]\[ P(\text{number} > 5) = \frac{1}{6} \][/tex]
3. Calculate the combined probability of flipping "heads" and rolling a number greater than 5:
- Since the coin flip and the die roll are independent events, the combined probability is the product of the individual probabilities:
[tex]\[ P(\text{heads and number} > 5) = P(\text{heads}) \times P(\text{number} > 5) = \frac{1}{2} \times \frac{1}{6} \][/tex]
- Simplify the multiplication:
[tex]\[ P(\text{heads and number} > 5) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \][/tex]
Therefore, the probability that you flip "heads" and roll a number greater than 5 is [tex]\(\frac{1}{12}\)[/tex].
The correct answer is:
[tex]\[ \boxed{\frac{1}{12}} \][/tex]
1. Determine the probability of flipping "heads" on the coin:
- A standard coin has two sides, "heads" and "tails". Therefore, the probability of flipping "heads" is:
[tex]\[ P(\text{heads}) = \frac{1}{2} \][/tex]
2. Determine the probability of rolling a number greater than 5 on the die:
- A standard die has six sides, numbered 1 through 6.
- The numbers greater than 5 are just 6.
- There is only 1 favorable outcome (rolling a 6) out of 6 possible outcomes. Therefore, the probability of rolling a number greater than 5 is:
[tex]\[ P(\text{number} > 5) = \frac{1}{6} \][/tex]
3. Calculate the combined probability of flipping "heads" and rolling a number greater than 5:
- Since the coin flip and the die roll are independent events, the combined probability is the product of the individual probabilities:
[tex]\[ P(\text{heads and number} > 5) = P(\text{heads}) \times P(\text{number} > 5) = \frac{1}{2} \times \frac{1}{6} \][/tex]
- Simplify the multiplication:
[tex]\[ P(\text{heads and number} > 5) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \][/tex]
Therefore, the probability that you flip "heads" and roll a number greater than 5 is [tex]\(\frac{1}{12}\)[/tex].
The correct answer is:
[tex]\[ \boxed{\frac{1}{12}} \][/tex]
