(B) Let $A$ be the event that a person has brown hair and $B$ be the event that a person has brown eyes.Given:$P(A) = 40/100 = 0.4$$P(B) = 25/100 = 0.

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Let $A$ be the event that a person has brown hair and $B$ be the event that a person has brown eyes.Given:$P(A) = 40/100 = 0.4$$P(B) = 25/100 = 0.25$$P(A \cap B) = 15/100 = 0.15$We need to find the conditional probability $P(B|A)$,which is the probability that a person has brown eyes given that they have brown hair.The formula for conditional probability is $P(B|A) = \frac{P(A \cap B)}{P(A)}$.Substituting the values:$P(B|A) = \frac{0.15}{0.40} = \frac{15}{40} = \frac{3}{8}$.Thus,the probability is $3/8$.

Class 12 Mathematics Probability Conditional probability

Easy

In a certain town,$40\%$ of the people have brown hair,$25\%$ have brown eyes,and $15\%$ have both brown hair and brown eyes. If a person selected at random from the town has brown hair,what is the probability that they also have brown eyes?

A
$1/5$
B
$3/8$
C
$1/3$
D
$2/3$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Conditional probability

$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is:

DifficultJEE MAIN 2021

View Solution

$A$ black and a red dice are rolled. Find the conditional probability of obtaining the sum $8$,given that the red die resulted in a number less than $4$.

Medium

View Solution

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$,and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$,then the value of $\frac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is:

DifficultJEE MAIN 2025

View Solution

$A$ couple has two children. Find the probability that both children are males,if it is known that at least one of the children is male.

Medium

View Solution

Suppose that $E_1$ and $E_2$ are two events of a random experiment such that $P(E_1) = \frac{1}{4}$,$P(E_2 / E_1) = \frac{1}{2}$ and $P(E_1 / E_2) = \frac{1}{4}$. Observe the lists given below. The correct matching of List-$I$ with List-$II$ is:
List-$I$ List-$II$
$(A)$ $P(E_2)$ $(i)$ $1/4$
$(B)$ $P(E_1 \cup E_2)$ $(ii)$ $5/8$
$(C)$ $P(\bar{E}_1 / \bar{E}_2)$ $(iii)$ $1/8$
$(D)$ $P(E_1 / \bar{E}_2)$ $(iv)$ $1/2$
$(v)$ $3/8$
$(vi)$ $3/4$

DifficultTS EAMCET 2009

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

List-$I$	List-$II$
$(A)$ $P(E_2)$	$(i)$ $1/4$
$(B)$ $P(E_1 \cup E_2)$	$(ii)$ $5/8$
$(C)$ $P(\bar{E}_1 / \bar{E}_2)$	$(iii)$ $1/8$
$(D)$ $P(E_1 / \bar{E}_2)$	$(iv)$ $1/2$
	$(v)$ $3/8$
	$(vi)$ $3/4$

In a certain town,$40\%$ of the people have brown hair,$25\%$ have brown eyes,and $15\%$ have both brown hair and brown eyes. If a person selected at random from the town has brown hair,what is the probability that they also have brown eyes?

Similar Questions

$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is:

$A$ black and a red dice are rolled. Find the conditional probability of obtaining the sum $8$,given that the red die resulted in a number less than $4$.

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$,and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$,then the value of $\frac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is:

$A$ couple has two children. Find the probability that both children are males,if it is known that at least one of the children is male.

Vedclass Test Series

Exam Paper Generator

Online Exam Module