Question

craig flips a coin and rolls a 6-sided die 30 times. the sample space for his experiment is below. what is the empirical probability of the experiment for flipping a head and rolling a 1?

craigs experiment
sample space

h 3 | t 2 | t 3 | t 6 | t 6 | t 3
h 1 | t 2 | h 1 | h 5 | h 4 | h 1
t 4 | h 2 | t 3 | h 5 | h 4 | t 3
t 6 | t 3 | h 4 | t 1 | h 3 | h 2
t 6 | h 2 | h 6 | t 6 | h 1 | h 1

\\(\bigcirc \frac{1}{2}\\)
\\(\bigcirc \frac{1}{6}\\)
\\(\bigcirc \frac{1}{4}\\)
\\(\bigcirc \frac{1}{12}\\)

Explanation:

Count the total number of trials

$$ N = 30 $$

Count the occurrences of flipping a Head and rolling a 1 (H1)

$$ \text{Occurrences of H1} = 5 \quad (\text{found at row 2 col 1, row 2 col 3, row 2 col 6, row 5 col 5, row 5 col 6}) $$

Calculate the empirical probability

$$ P(\text{H1}) = \frac{5}{30} = \frac{1}{6} $$

Answer:

• (A) \(\frac{1}{2}\)
• (B) \(\frac{1}{6}\) (Correct answer)
• (C) \(\frac{1}{4}\)
• (D) \(\frac{1}{12}\)