Question

1. you flip a coin 10 times and observe heads 7 times. how does this compare to the theoretical probability?

a. theoretical and empirical probabilities are the same.
b. empirical probability is higher than theoretical.
c. theoretical probability is higher than empirical.
d. empirical and theoretical probabilities cannot be compared.

Explanation:

Step1: Calculate theoretical probability

A fair coin has 2 possible outcomes (heads or tails). The theoretical probability of getting heads, \(P(\text{heads})\) is \(\frac{1}{2}=0.5\)

Step2: Calculate empirical probability

Empirical probability \(P_{e}=\frac{\text{Number of heads}}{\text{Total number of flips}}\). Here, number of heads \(= 7\), total flips \(=10\). So \(P_{e}=\frac{7}{10} = 0.7\)

Step3: Compare the two probabilities

Since \(0.7>0.5\) (i.e., \(P_{e}>P\))

Answer:

B. Empirical probability is higher than theoretical.