Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black ba

Sail E0 Webinar

Question

Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. If one ball is now drawn at random from urn A, the probability that it is found to be red, is

Options:

A .

\frac{32}{55}

B .

\frac{21}{55}

C .

\frac{19}{55}

D . None of these

Answer: Option D
:
D

Let the events are
$R_{1}$ = A red ball is drawn from urn A and placed in B
$B_{1}$ = A black ball is drawn from urn A and placed in B
$R_{2}$ = A red ball is drawn from urn A and placed in A
$B_{2}$ = A black ball is drawn from urn A and placed in B
R = A red ball is drawn in the second attempt from A
Then the required probability
$= P (R_{1} R_{2} R) + (R_{1} B_{2} R) + P (B_{1} R_{2} R) + P (B_{1} B_{2} R)$
$= P (R_{1}) P (R_{2}) P (R) + P (R_{1}) P (B_{2}) P (R) + P (B_{1}) P (R_{2}) P (R) + P (B_{1}) P (B_{2}) P (R)$

$= \frac{6}{10} \times \frac{5}{11} \times \frac{6}{10} \times \frac{6}{10} \times \frac{6}{11} \times \frac{5}{10} \times \frac{4}{10} \times \frac{4}{11} \times \frac{7}{10} + \frac{4}{10} \times \frac{7}{11} \times \frac{6}{10}$
$= \frac{32}{55}$

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. One of the two events must occur. If the chance of one is 23 of the other, then odds in favour of the other are ....the other, then odds in favour of the other are

Question 2. If A and B are two events such that P(A) = 12 and P(B) = 23, then ....

Question 3. The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays is ____. ....

Question 4. Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from ur....the probability that it is found to be red, is

Question 5. One of the two events must occur. If the chance of one is 23 of the other, then odds in favour of the other are ....the other, then odds in favour of the other are

Question 6. The probability of a bomb hitting a bridge is 12 and two direct hits are needed to destroy it. The least number of bom....of the bridge beeing destroyed is greater then 0.9, is

Question 7. The probability of happening an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, th....events, then the probability of happening neither A nor B is

Question 8. If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7m....that a number of the form 7m+7n is divisible by 5 equals

Question 9. The probability that A speaks truth is 45, while this probability for B is 34. The probability that they contradict ea....each other when asked to speak on a fact is

Question 10. Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consu....that all the three apply for the same house is

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

GPOE / GPA Combined 1 Free Mock Test SAIL JO E-0 2024

ICA Combined 1 Free Revision Test SAIL JO E-0

RDIC Review Test SAIL JO E-0

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

RSP Combined 1 Free Revision Test SAIL JO E-0