Step 1: Given information

Probability of event A is \(\displaystyle{\frac{{{3}}}{{{4}}}}\)

Probability of event B is \(\displaystyle{\frac{{{1}}}{{{4}}}}\)

Step 2: Answer is given by,

The probability of both A and B occurring at the same time is given by,

\(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={P}{\left({A}\right)}{P}{\left({B}\right)}\)

\(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={\frac{{{3}}}{{{4}}}}\times{\frac{{{1}}}{{{4}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of both A and B occurring at the same time is \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

Option (C) is correct.

Probability of event A is \(\displaystyle{\frac{{{3}}}{{{4}}}}\)

Probability of event B is \(\displaystyle{\frac{{{1}}}{{{4}}}}\)

Step 2: Answer is given by,

The probability of both A and B occurring at the same time is given by,

\(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={P}{\left({A}\right)}{P}{\left({B}\right)}\)

\(\displaystyle{P}{\left({A}\ {\quad\text{and}\quad}\ {B}\right)}={\frac{{{3}}}{{{4}}}}\times{\frac{{{1}}}{{{4}}}}={\frac{{{3}}}{{{16}}}}\)

The probability of both A and B occurring at the same time is \(\displaystyle{\frac{{{3}}}{{{16}}}}\)

Option (C) is correct.