Question

A fair coin is tossed five times. Calculate the probability that it lands head-up at least twice.

• A. $\frac{3}{16}$
• B. $\frac{1}{4}$
• C. $\frac{7}{16}$
• D. $\frac{13}{16}$
• E. $\frac{27}{32}$

Answer 1

Answer: (D)

$\frac{13}{16}$

We have to find probability that the coin lands head-up at least twice, now we will find probability of $1$ head and probability of $0$ heads and we will subtract it with $1$.
Probability of $0$ heads is ${\left(\frac{1}{2}\right)}^5$.
Probability of $1$ heads is $5\times {\left(\frac{1}{2}\right)}^5$.
Therefore, required probability is $1-\frac{1}{32}-\frac{5}{32}=\frac{26}{32}=\frac{13}{32}$.