Question

you flip a coin 10 times and observe heads 7 times. how does this compare to the theoretical probability?
a. theoretical probability is higher than empirical.
b. empirical probability is higher than theoretical.
c. empirical and theoretical probabilities cannot be compared.
d. theoretical and empirical probabilities are the same.

Explanation:

Step1: Calculate theoretical probability

The theoretical probability of getting heads when flipping a fair coin is \( P(\text{heads})=\frac{1}{2} = 0.5\)

Step2: Calculate empirical probability

The empirical probability is \( P(\text{heads})=\frac{\text{Number of heads}}{\text{Total flips}}=\frac{7}{10}=0.7\)

Step3: Compare the two probabilities

Since \(0.7>0.5\), the empirical probability is higher than the theoretical probability.

Answer:

b. Empirical probability is higher than theoretical.