# A Coin is Tossed 4 Times. the Probability that at Least One Head Turns up is - Mathematics

MCQ

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

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

Concept: Bernoulli Trials and Binomial Distribution
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 22 | Page 29