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A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.?
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The problem provides information about a bag containing 18 balls, out of which a certain number of balls are red. We need to find the probability of drawing a non-red ball from the bag and determine the value of x.
i) Probability of drawing a non-red ball:
To find the probability of drawing a non-red ball, we need to determine the number of non-red balls in the bag. Since we know that the bag contains 18 balls in total, the number of non-red balls can be calculated as 18 - x (where x represents the number of red balls).
The probability of drawing a non-red ball can be calculated by dividing the number of non-red balls by the total number of balls in the bag. Therefore, the probability of drawing a non-red ball is given by:
P(non-red) = (18 - x)/18
ii) Probability of drawing a red ball after adding two more red balls:
After adding two more red balls to the bag, the total number of red balls in the bag will be x + 2. The total number of balls in the bag will also increase by 2, making it 20.
The probability of drawing a red ball in this case is given as 9/8 times the probability in the first case. Therefore, we can write the equation:
(9/8) * P(red) = P(red after adding two balls)
To find the value of x, we need to solve this equation.
Solving the equation:
First, let's find the probability of drawing a red ball in the first case. The probability of drawing a red ball can be calculated by subtracting the probability of drawing a non-red ball from 1 (since there are only two possibilities - either the ball is red or non-red). Therefore:
P(red) = 1 - P(non-red)
= 1 - (18 - x)/18
= (18 - 18 + x)/18
= x/18
Now, let's substitute this value into the equation for the second case:
(9/8) * (x/18) = (x + 2)/20
We can solve this equation to find the value of x.
Cross-multiply and simplify:
(9/8) * (x/18) = (x + 2)/20
(9/8) * x * 20 = (x + 2) * 18
(9 * 20 * x) / 8 = (x + 2) * 18
(9 * 5 * x) / 2 = (x + 2) * 18
(45 * x) / 2 = 18x + 36
45x = 36 * 2x + 36 * 2
45x = 72x + 72
45x - 72x = 72
-27x = 72
x = -72/27
x ≈ -2.67
Since the number of balls cannot be negative, we can conclude that there is no valid value of x that satisfies the given conditions.
Hence, there is no solution for the value of x in this scenario.
i) Probability of drawing a non-red ball:
To find the probability of drawing a non-red ball, we need to determine the number of non-red balls in the bag. Since we know that the bag contains 18 balls in total, the number of non-red balls can be calculated as 18 - x (where x represents the number of red balls).
The probability of drawing a non-red ball can be calculated by dividing the number of non-red balls by the total number of balls in the bag. Therefore, the probability of drawing a non-red ball is given by:
P(non-red) = (18 - x)/18
ii) Probability of drawing a red ball after adding two more red balls:
After adding two more red balls to the bag, the total number of red balls in the bag will be x + 2. The total number of balls in the bag will also increase by 2, making it 20.
The probability of drawing a red ball in this case is given as 9/8 times the probability in the first case. Therefore, we can write the equation:
(9/8) * P(red) = P(red after adding two balls)
To find the value of x, we need to solve this equation.
Solving the equation:
First, let's find the probability of drawing a red ball in the first case. The probability of drawing a red ball can be calculated by subtracting the probability of drawing a non-red ball from 1 (since there are only two possibilities - either the ball is red or non-red). Therefore:
P(red) = 1 - P(non-red)
= 1 - (18 - x)/18
= (18 - 18 + x)/18
= x/18
Now, let's substitute this value into the equation for the second case:
(9/8) * (x/18) = (x + 2)/20
We can solve this equation to find the value of x.
Cross-multiply and simplify:
(9/8) * (x/18) = (x + 2)/20
(9/8) * x * 20 = (x + 2) * 18
(9 * 20 * x) / 8 = (x + 2) * 18
(9 * 5 * x) / 2 = (x + 2) * 18
(45 * x) / 2 = 18x + 36
45x = 36 * 2x + 36 * 2
45x = 72x + 72
45x - 72x = 72
-27x = 72
x = -72/27
x ≈ -2.67
Since the number of balls cannot be negative, we can conclude that there is no valid value of x that satisfies the given conditions.
Hence, there is no solution for the value of x in this scenario.
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A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.?
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A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.?.
A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 18 balls out of which x balls are red. i) if one ball is drawn at random from the bag, what is the probablity that it is not red. ii) if two more red balls are put in the bag, the probablity of drawing a red ball will be 9/8 times the probablity of drawing a red ball in the first case find the value of x.?.
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