Question

what is the theoretical probability of flipping a heads on a fair coin?
a. $\frac{1}{2}$
b. $\frac{1}{4}$
c. $\frac{3}{4}$
d. $\frac{1}{3}$

Explanation:

Step1: Determine total outcomes

A fair coin has 2 possible outcomes: heads (H) or tails (T). So, total number of outcomes \( n(S)=2 \).

Step2: Determine favorable outcomes

The favorable outcome (getting heads) is 1. So, number of favorable outcomes \( n(E) = 1 \).

Step3: Use probability formula

The formula for theoretical probability is \( P(E)=\frac{n(E)}{n(S)} \). Substituting the values, we get \( P(E)=\frac{1}{2} \).

Answer:

A. \( \frac{1}{2} \)