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2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?
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2 A bag contains only red and blue marbles. Yasmine takes one marble a...
Let the no. of red marbles = n.....and that of blue marbles = y....then in 1st situation..prob of taking red ball = n/(n+y) = 1/5...let n+y be x so that 5n=x.......and when 5more red marbles are added to the bag..then the prob of taking out the red marbl becomes = (n+5)/(5n+5 )=1/3...by solving this eq... n= 5....then from the eq 5n= x ...we get x= 25.... and x= n+y....therefore y= 20...so no. of red marbles =5 ... and blue =20
Community Answer
2 A bag contains only red and blue marbles. Yasmine takes one marble a...
Given Information:
- The probability of picking a red marble from the bag initially is 1 in 5.
- Yasmine returns the marble to the bag and adds five more red marbles.
- The probability of picking a red marble from the bag after adding the extra red marbles is 1 in 3.
Let's solve the problem step by step:
Step 1: Determine the initial probability of picking a red marble:
- Let's assume there are 'r' red marbles and 'b' blue marbles in the bag initially.
- The total number of marbles in the bag is 'r + b'.
- The probability of picking a red marble initially can be expressed as: P(red) = r / (r + b).
- According to the problem, P(red) = 1/5.
Step 2: Determine the probability of picking a red marble after adding the extra marbles:
- Yasmine returns the marble to the bag, so the total number of marbles in the bag remains the same.
- Yasmine adds five more red marbles to the bag, resulting in 'r + 5' red marbles in the bag.
- The probability of picking a red marble after adding the extra marbles can be expressed as: P(red) = (r + 5) / (r + 5 + b).
- According to the problem, P(red) = 1/3.
Step 3: Solve the equations:
- We have two equations with two unknowns: r / (r + b) = 1/5 and (r + 5) / (r + 5 + b) = 1/3.
- Let's solve these equations to find the values of 'r' and 'b'.
Step 4: Solve equation 1:
- Multiply both sides of the equation by (r + b) to eliminate the denominator: r = (r + b) / 5.
Step 5: Solve equation 2:
- Multiply both sides of the equation by (r + 5 + b) to eliminate the denominator: r + 5 = (r + 5 + b) / 3.
Step 6: Simplify equation 4:
- Multiply both sides of the equation by 5 to eliminate the fraction: 5r = r + b.
Step 7: Simplify equation 5:
- Multiply both sides of the equation by 3 to eliminate the fraction: 3(r + 5) = r + 5 + b.
Step 8: Simplify equation 6:
- Distribute 3 on the left side of the equation: 3r + 15 = r + 5 + b.
Step 9: Simplify equation 7:
- Combine like terms on the right side of the equation: 3r + 15 = r + b + 5.
Step 10: Simplify equation 8:
- Subtract r from both sides of the equation: 2r + 15 = b + 5.
Step 11: Simplify equation 9:
- Subtract 5 from both sides of the equation: 2r
- The probability of picking a red marble from the bag initially is 1 in 5.
- Yasmine returns the marble to the bag and adds five more red marbles.
- The probability of picking a red marble from the bag after adding the extra red marbles is 1 in 3.
Let's solve the problem step by step:
Step 1: Determine the initial probability of picking a red marble:
- Let's assume there are 'r' red marbles and 'b' blue marbles in the bag initially.
- The total number of marbles in the bag is 'r + b'.
- The probability of picking a red marble initially can be expressed as: P(red) = r / (r + b).
- According to the problem, P(red) = 1/5.
Step 2: Determine the probability of picking a red marble after adding the extra marbles:
- Yasmine returns the marble to the bag, so the total number of marbles in the bag remains the same.
- Yasmine adds five more red marbles to the bag, resulting in 'r + 5' red marbles in the bag.
- The probability of picking a red marble after adding the extra marbles can be expressed as: P(red) = (r + 5) / (r + 5 + b).
- According to the problem, P(red) = 1/3.
Step 3: Solve the equations:
- We have two equations with two unknowns: r / (r + b) = 1/5 and (r + 5) / (r + 5 + b) = 1/3.
- Let's solve these equations to find the values of 'r' and 'b'.
Step 4: Solve equation 1:
- Multiply both sides of the equation by (r + b) to eliminate the denominator: r = (r + b) / 5.
Step 5: Solve equation 2:
- Multiply both sides of the equation by (r + 5 + b) to eliminate the denominator: r + 5 = (r + 5 + b) / 3.
Step 6: Simplify equation 4:
- Multiply both sides of the equation by 5 to eliminate the fraction: 5r = r + b.
Step 7: Simplify equation 5:
- Multiply both sides of the equation by 3 to eliminate the fraction: 3(r + 5) = r + 5 + b.
Step 8: Simplify equation 6:
- Distribute 3 on the left side of the equation: 3r + 15 = r + 5 + b.
Step 9: Simplify equation 7:
- Combine like terms on the right side of the equation: 3r + 15 = r + b + 5.
Step 10: Simplify equation 8:
- Subtract r from both sides of the equation: 2r + 15 = b + 5.
Step 11: Simplify equation 9:
- Subtract 5 from both sides of the equation: 2r
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2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?
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2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?.
2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?.
Solutions for 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? in English & in Hindi are available as part of our courses for Class 11.
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Here you can find the meaning of 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? defined & explained in the simplest way possible. Besides giving the explanation of
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ample number of questions to practice 2 A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag? tests, examples and also practice Class 11 tests.
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