Question

The probability of getting atleast one tail in $4$ throws of a coin is

• A. $\frac{15}{16}$
• B. $\frac{1}{16}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

The correct option is A

$\frac{15}{16}$

Calculate the probability

Whenever we throw a coin, the probability of getting Tails is $\frac{1}{2}$

So, in the event of getting tails in $4$ throws is $A$ and probability is $P\left(A\right)$

$\therefore P\left(A\right)$$={\left(\frac{1}{2}\right)}^4=\frac{1}{16}$

Again, the event of getting atleast one tail in $4$ throws is $A^{\text{'}}$ and probability is $P\left(A^{\text{'}}\right)$

Now, we know that ,

$$\begin{gathered} P\left(A\right)+P\left(A\text{'}\right)=1 \\ \Rightarrow P\left(A^{\text{'}}\right)=1-P\left(A\right) \\ \Rightarrow P\left(A^{\text{'}}\right)=1-\frac{1}{16} \\ \Rightarrow P\left(A^{\text{'}}\right)=\frac{16-1}{16} \\ \Rightarrow P\left(A^{\text{'}}\right)=\frac{15}{16} \end{gathered}$$

Therefore, the probability of getting atleast one tail in $4$ throws of a coin is $\frac{15}{16}$, option (A) is the correct answer.