Question

In an experiment of tossing a coin, if head is obtained then the coin is tossed again and if tail is obtained then a die is rolled. What is the probability of obtaining a tail on the coin and number $3$ on the die?

• A. $\frac{1}{8}$
  
• B. $\frac{1}{6}$
  
• C. $\frac{1}{2}$
  
• D. $\frac{1}{12}$
  

Answer 1

The correct option is D $\frac{1}{12}$


The experiment performed can be shown as:



Let $\text{P(T)}$ denotes the probability of obtaining a tail on the coin in the beginning.
$\text{P(T)}=\frac{{}^1{C}_1}{{}^2{C}_1}$
$\text{P(T)}=\frac{1}{2}$

Let $\text{P(3)}$ denotes the probability of obtaining number $3$ on the die.
$\text{P(3)}=\frac{{}^1{C}_1}{{}^6{C}_1}$
$\text{P(3)}=\frac{1}{6}$


Let $\text{P(T and 3)}$ denotes the probability of obtaining tail on the coin and number $3$ on the die.
$\text{P(T and 3)}=\text{P(T)}\times \text{P(3)}$
$=\frac{1}{2}\times \frac{1}{6}$
$=\frac{1}{12}$

The probability of obtaining tail on the coin and number $3$ on the die is $\frac{1}{12}$.

Therefore, option (d.) is the correct answer.