8. to play a game, a number cube with sides n...
8. to play a game, a number cube with sides numbered 1 through 6 is rolled and a fair coin is flipped. use a table to represent the sample space. what is the probability of flipping a head and rolling either a 3 or a 5? write a percent rounded to the nearest tenth.
Answer
# Explanation:
## Step1: Determine the total number of outcomes
The number of outcomes when rolling a number cube is \(n_{cube}=6\) (since the cube has 6 sides numbered 1 - 6). The number of outcomes when flipping a coin is \(n_{coin}=2\) (head or tail).
By the fundamental counting principle, the total number of outcomes in the sample space \(n = n_{cube}\times n_{coin}=6\times2 = 12\).
## Step2: Determine the number of favorable outcomes
The favorable outcomes are (H, 3) and (H, 5). So the number of favorable outcomes \(m = 2\).
## Step3: Calculate the probability
The probability formula is \(P=\frac{m}{n}\). Substituting \(m = 2\) and \(n=12\), we get \(P=\frac{2}{12}=\frac{1}{6}\).
## Step4: Convert the probability to a percentage
To convert \(\frac{1}{6}\) to a percentage, we use the formula \(P(\%)=\frac{1}{6}\times100\%\).
\(P(\%)=\frac{100}{6}\% \approx 16.7\%\)
# Answer:
\(16.7\%\)