#### Question

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

##### Options

\[\frac{1}{16}\]

\[\frac{2}{16}\]

\[\frac{14}{16}\]

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

#### Solution

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

Let *X* denote the number of heads obtained in four tosses of a coin .

Then *X* follows a binomial distribution with

\[n = 4 \text{ and } p = q = \frac{1}{2}\]

\[\text{ Distribution is given by } \]

\[P(X = r) = ^{4}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{4 - r} \]

\[ \therefore P(X = r) = ^{4}{}{C}_0 \left( \frac{1}{2} \right)^0 \left( \frac{1}{2} \right)^{4 - 0} \]

\[P(\text{ atleast one head turns up} ) = P(X \geq 1) \]

\[ = 1 - P(X = 0) \]

\[ = 1 - \frac{1}{2^4}\]

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

Is there an error in this question or solution?

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A Coin is Tossed 4 Times. the Probability that at Least One Head Turns up is Concept: Bernoulli Trials and Binomial Distribution.

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