Question

When a certain coin is flipped, the probability of obtaining a tails is $0.60$. Which of the following is the probability that tails would be obtained exactly $10$ times when the coin is flipped $20$ times?

• A. $0.0473$
• B. $0.1171$
• C. $0.1762$
• D. $0.2447$
• E. $0.50$

Answer 1

The correct option is B

$0.1171$

Explanation for the correct answer:

Step-1: Finding the probability of obtaining a head:

Given that the probability of obtaining a tail when a certain coin is flipped is $q=0.60$.

We know that if the probability of obtaining a head is $p$, then

$$\begin{gathered} p+q=1 \\ \Rightarrow p=1-q \end{gathered}$$

Now, as $q=0.60$, the probability of obtaining a head will be

$$\begin{gathered} p=1-q \\ =1-0.60 \\ =0.40 \end{gathered}$$

Step-2: Finding the probability of getting exactly $10$ tails when a coin is flipped $20$ times:

Formula to be used : We know that if the probability of obtaining a head is $p$ and the probability of getting a tail is $q$, then the probability of obtaining exactly $m$ tails when a coin is flipped $n$ times is given by

$P={}^{n}C_{n-m}{p}^{n-m}{q}^m$.

Here, $n=20$ and $m=10$, $p=0.40$ and $q=0.60$.

Hence, the required probability is

$$\begin{gathered} P={}^{n}C_{n-m}{p}^{n-m}{q}^m \\ ={}^{20}C_{20-10}{\left(0.40\right)}^{20-10}{\left(0.60\right)}^{10} \\ =\frac{20!}{10!\times 10!}\times {\left(0.40\right)}^{10}\times {\left(0.60\right)}^{10} \\ =0.1171 \end{gathered}$$

Hence, option (B) is the correct answer.