Question

A coin is tossed 4 times. The probability that at least one head turns up is

Options

• \[\frac{1}{16}\]

   

• \[\frac{2}{16}\]

   

• \[\frac{14}{16}\]

   

• \[\frac{15}{16}\]

   

Answer 1

\[\frac{15}{16}\]

Let X denote the number of heads obtained in four tosses of a coin .
Then X follows a binomial distribution with

\[n = 4 \text{ and } p = q = \frac{1}{2}\]
\[\text{ Distribution is given by } \]
\[P(X = r) = ^{4}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{4 - r} \]
\[ \therefore P(X = r) = ^{4}{}{C}_0 \left( \frac{1}{2} \right)^0 \left( \frac{1}{2} \right)^{4 - 0} \]
\[P(\text{ atleast one head turns up} )  = P(X \geq 1) \]
\[ = 1 - P(X = 0) \]
\[ = 1 - \frac{1}{2^4}\]
\[ = \frac{15}{16}\]