Question

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

• A. $\frac{1}{32}$
• B. $\frac{13}{32}$
• C. $\frac{16}{32}$
• D. $\frac{31}{32}$

Answer 1

The correct option is D $\frac{31}{32}$

For an unbiased coin, probability of getting head or tail are
$P\left(H\right)=\frac{1}{2},\text{and}P\left(T\right)=\frac{1}{2}$

Coin is tossed five times. Hence the probability of getting at least one head

P = 1 - (Probability of not getting any head)

$=1-{\left(\frac{1}{2}\right)}^5=1-\frac{1}{32}$

$\Rightarrow P=\frac{31}{32}$