A Bag Contains 3 Red and 2 Black Ball. Another Bag Contains 4 Red and 5 Black Balls GMAT Problem Solving

Question: A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?

1. 3/5
2. 2/5
3. 4/25
4. 3/10
5. 15/23

Correct Answer: E
Solution and Explanation:

Approach Solution 1:
Given:
Bag 1: 3 Red, 2 Black
Bag 2: 4 Red, 5 Black

1st transaction:
A ball is moved from bag 1 and shifted to bag 2
P(R)= 3/5 and P(B)= ⅖

2nd Transaction:
A ball is picked from Bag 2.

Required: Probability that this draw of red ball is due to the drawing of red ball from the first bag

Case 1: Black ball was picked from Bag 1 and then a Red is picked from Bag 2
P(R) = 2/5∗4/10= 8/50
Case 2: Red ball was picked from Bag 1 and then a Red is picked from Bag 2
P(R)= 3/5*5/10= 15/50

We need the probability of occurrence off Case 2:
Hence P(Case 2)= 15/50 / (8/50+15/50)= 15/23

Approach Solution 2:
Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50
Probability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50

Now comes the condition, hence apply conditional probability:
P(Red)/ P(Red + Black)
(15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23.

Approach Solution 3:
The ball transferred from the first bag to the second could be a black ball or a red ball. Therefore, we have two scenarios:

1) A red ball is drawn from the 2nd bag after a black ball is drawn from 1st bag and transferred to the 2nd bag.
2) A red ball is drawn from the 2nd bag after a red ball is drawn from 1st bag and transferred to the 2nd bag.

Let’s find the probability of each scenario:

1) P(1st = black, 2nd = red) = 2/5 x 4/10 = 8/50
2) P(1st = red, 2nd = red) = 3/5 x 5/10 = 15/50

Thus the probability of drawing a red ball from the 2nd bag is 8/50 + 15/50 = 23/50, and the probability that it is due to a red ball having been drawn from the 1st bag is:
(15/50)/(23/50) = 15/23

“A bag contains 3 red and 2 black ball. Another bag contains 4 red and”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

Suggested GMAT Problem Solving Samples

• The Greatest 6-Digit Number When Divided by 6, 7 ,8 , 9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8 Respectively GMAT Problem Solving
• Is Zero Even Integer or Odd Integer? GMAT Problem Solving
• If 20 Men or 24 Women or 40 Boys can do a Job in 12 Days GMAT Problem Solving
• If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal?
• How many Terminating Zeroes does 200 Have GMAT Problem Solving
• Properties of Circle GMAT Problem Solving
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible? GMAT Problem Solving
• For How Many Values of k is 12^12 the Least Common Multiple GMAT Problem Solving
• Bag A Contains Red, White and Blue Marbles such that GMAT Problem Solving
• Assume that all 7-Digit Numbers That do not Begin with 0 or 1 are Valid Phone Numbers. GMAT Problem Solving
• A Car Travels from Mayville to Rome at an Average Speed of 30 miles per hour GMAT Problem Solving
• A Certain Sum of Money is Divided Among A, B and C such that A Gets One GMAT Problem Solving
• The Ratio of Boys to Girls in Class A is 1 to 4, and that in Class B is 2 to 5 GMAT Problem Solving
• The Maximum Mark in an Examination is 100 and the Minimum is 0 GMAT Problem Solving
• A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving
• A Driver Completed the First 20 Miles of a 40-Mile Trip at an Average Speed of 50 Miles Per Hour GMAT Problem Solving
• The sum of three numbers is 98. If the ratio between first and second be 2:3 and between second and third be 5:8 GMAT Problem Solving
• How Many Three-Letter Words Can be Constructed Using All the 26 Letters of the English Alphabet GMAT Problem Solving
• How Many Litres of Pure Alcohol Must be Added to a 100-litre Solution That is 20 Percent Alcohol GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
• How Many Five Digit Numbers Can be Formed Using Digits 0, 1, 2, 3, 4, 5, Which Are Divisible By 3 GMAT Problem Solving
• An “Armstrong Number” is an n-Digit Number That is Equal to the Sum of the nth Powers GMAT Problem Solving
• A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds
• A Train can Travel 50% Faster than a Car GMAT Problem Solving
• A rectangle is inscribed in a hexagon that has all sides of equal length and all angles of equal measure GMAT Problem Solving
• A Positive Integer Is Divisible by 9 If And Only If The Sum of Its Digits is Divisible By 9 GMAT Problem Solving
• The two lines are tangent to the circle. GMAT Problem Solving
• In a Certain Population, There are 3 Times as Many People Aged Twenty-One or Under GMAT Problem Solving
• In How Many Different Ways can 3 Identical Green Shirts and 3 Identical Red Shirts be Distributed Among 6 Children GMAT Problem Solving
• The Value Of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 Is GMAT Problem Solving
• Points A And B Are 120 Km Apart. A Motorcyclist Starts From GMAT Problem Solving
• A student took five papers in an examination, where the full marks GMAT Problem Solving
• In how many ways can letters the word ATTITUDE be rearranged such that GMAT Problem Solving
• A merchant mixes three varieties of rice costing $20/kg, $24/kg GMAT Problem Solving
• ABC is an equilateral triangle, and point D is the midpoint of side BC GMAT Problem Solving
• A Batsman Makes a Score of 87 Runs in the 17th Match and Thus Increases GMAT Problem Solving
• If M= √4+3√4+4√4, Then the Value of M is GMAT Problem Solving
• An Octagon Is Inscribed In A Circle As Shown Above. What Of The Area GMAT Problem Solving
• In a Company of Only 20 Employees, 10 Employees make $80,000/yr GMAT Problem Solving
• A bag contains blue and red balls only GMAT Problem Solving
• (4.8*10^9)^(1/2) is closest in value to GMAT Problem Solving
• What Is The Units Digit Of 2222^333 ∗ 3333^222? GMAT Problem Solving
• What Is The Tens Digit Of 6^17? GMAT Problem Solving
• If m=−2, What Is −m^(−m)? GMAT Problem Solving
• An Automated Manufacturing Plant Uses Robots To Manufacture Products GMAT Problem Solving
• The Surface Distance Between 2 Points on the Surface of a Cube is the GMAT Problem Solving
• The Average Monthly Expenditure of a Family for the First Four Months GMAT Problem Solving
• When a Certain Perfect Square is Increased by 148, the Result is GMAT Problem Solving
• If p#q Denotes the Least Common Multiple of p and q, Then ((12#16) GMAT Problem Solving
• The Smallest of Six Consecutive Odd Integers Whose Average (arithmetic mean) is x + 2 GMAT Problem Solving