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

kdgg0909gn 2021-11-20 Answered
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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Expert Answer

Thouturs
Answered 2021-11-21 Author has 941 answers
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.
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