 Questions & Answers    Question Answers

# If $4P(A) = 6P(B) = 10P(A \cap B) = 1$ then $P(\frac{B}{A}) =$ -------.A.$\frac{2}{5}$B.$\frac{3}{5}$C.$\frac{7}{{10}}$D.$\frac{{19}}{{60}}$  Answer Verified
Hint: Here, to solve the given problem we use the conditional probability concept.

Given,
$4P(A) = 6P(B) = 10P(A \cap B) = 1 \to (1)$
Now, from equation 1, let us find ‘$P(A)$’, ‘$P(B)$’and ‘$P(A \cap B)$’ values.
$4P(A) = 1 \Rightarrow P(A) = \frac{1}{4}$
$6P(B) = 1 \Rightarrow P(B) = \frac{1}{6}$
$10P(A \cap B) = 1 \Rightarrow P(A \cap B) = \frac{1}{{10}}$
Here, we need to find the value of $P(B/A)$ i.e.., the probability of the event B after the
occurrence of event A.
So, to find the $P(B/A)$ let us consider the concept of conditional probability i.e..,
$P(B/A) = \frac{{P(A \cap B)}}{{P(A)}} \to (2)$
Let us substitute the obtained values of $P(A \cap B)$ and $P(A)$ in equation 2, we get

$\Rightarrow P(B/A) = \frac{{P(A \cap B)}}{{P(A)}} \\ \Rightarrow P(B/A) = \frac{{\frac{1}{{10}}}}{{\frac{1}{4}}} \\ \Rightarrow P(B/A) = \frac{4}{{10}} \\ \Rightarrow P(B/A) = \frac{2}{5} \\$
Hence, the obtained value of $P(B/A)$ is$\frac{2}{5}$.
Hence the correct option for the given question is ‘A’.
Note: As, to find the conditional probability of $P(B/A) = \frac{{P(A \cap B)}}{{P(A)}}$i.e.., the
probability of the event B after the occurrence of event A .The probability is defined only after the occurrence of event A i.e.., $P(A)$ should be greater than zero.

Bookmark added to your notes.
View Notes
Conditional Probability  Conditional Probability and It's Examples  Use of If Then Statements in Mathematical Reasoning  What is Mathematics?  Conditional Statement  What if the Earth Stopped Spinning?  What Happens if the Earth Stops Rotating?  CBSE Class 11 Maths Chapter 16 - Probability Formulas  CBSE Class 11 Maths Chapter 1 - Sets Formulas  Is 1 a Prime Number  