# if the probability of event A is \frac{3}{4} and the probability

if the probability of event A is $$\displaystyle{\frac{{{3}}}{{{4}}}}$$ and the probability of event B is 1/4 then the probability of both A and B occuring at the same time is
A)1 or absolute certainty
B) $$\displaystyle{\frac{{{1}}}{{{2}}}}$$
C) $$\displaystyle{\frac{{{3}}}{{{16}}}}$$
D) $$\displaystyle{\frac{{{3}}}{{{4}}}}$$
E) $$\displaystyle{\frac{{{1}}}{{{4}}}}$$

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Thouturs
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.