Question
If you toss a coin and roll a number cube, what is the probability of obtaining a head and rolling a 6? Round your answer to the nearest hundredth if using a decimal.
Answers
GPT-4o mini
To find the probability of both events occurring (tossing a head on a coin and rolling a 6 on a number cube), we can use the multiplication rule for independent events.
1. **Probability of tossing a head:** The probability of getting a head when tossing a fair coin is \( \frac{1}{2} \).
2. **Probability of rolling a 6:** The probability of rolling a 6 on a standard number cube (which has 6 faces) is \( \frac{1}{6} \).
Now, we multiply these probabilities together:
\[
P(\text{head and 6}) = P(\text{head}) \times P(\text{6}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]
To express this probability as a decimal, we can perform the division:
\[
\frac{1}{12} \approx 0.0833
\]
Rounding this value to the nearest hundredth, we get:
\[
0.08
\]
Thus, the probability of obtaining a head and rolling a 6 is **0.08**.
1. **Probability of tossing a head:** The probability of getting a head when tossing a fair coin is \( \frac{1}{2} \).
2. **Probability of rolling a 6:** The probability of rolling a 6 on a standard number cube (which has 6 faces) is \( \frac{1}{6} \).
Now, we multiply these probabilities together:
\[
P(\text{head and 6}) = P(\text{head}) \times P(\text{6}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
\]
To express this probability as a decimal, we can perform the division:
\[
\frac{1}{12} \approx 0.0833
\]
Rounding this value to the nearest hundredth, we get:
\[
0.08
\]
Thus, the probability of obtaining a head and rolling a 6 is **0.08**.