Question

If a fair coin is tossed 4 times, what is the probability that two heads and two tails will result?

• A. $\frac{1}{8}$
• B. $\frac{3}{8}$
• C. $\frac{5}{8}$
• D. $\frac{1}{2}$

Hint:

Exactly $k$ heads in $n$ tosses: $\binom{n}{k}/2^n$.

Answer 1

The Correct Option is B

Concept: This is a binomial probability problem where:
• Total trials = 4
• Probability of Head = $\frac{1}{2}$
• Probability of Tail = $\frac{1}{2}$

Step 1: Total possible outcomes \[ \text{Total outcomes} = 2^4 = 16 \]

Step 2: Favorable outcomes We want exactly 2 heads out of 4 tosses: \[ \text{Number of ways} = \binom{4}{2} = \frac{4!}{2!2!} = 6 \]

Step 3: Probability \[ P = \frac{6}{16} = \frac{3}{8} \] \[ \therefore \text{Correct answer is (B)} \]