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A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls?
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A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 bal...
Calculating the Probability of Drawing 2 Green Balls First:
To calculate the probability of drawing 2 green balls first, we first need to determine the total number of ways we can draw 2 balls out of 10 (6 blue and 4 green). This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!), where n is the total number of balls and r is the number of balls drawn.
In this case, C(10, 2) = 10! / (2!(10-2)!) = 45.
The number of ways to draw 2 green balls out of 4 is C(4, 2) = 6.
Therefore, the probability of drawing 2 green balls first is 6/45 = 2/15.
Calculating the Probability of Drawing 2 Blue Balls Second:
After drawing 2 green balls, there are now 8 balls remaining in the bag (4 blue and 4 green). We need to determine the probability of drawing 2 blue balls from these 8.
The total number of ways to draw 2 balls out of 8 is C(8, 2) = 28.
The number of ways to draw 2 blue balls out of 4 is C(4, 2) = 6.
Therefore, the probability of drawing 2 blue balls second is 6/28 = 3/14.
Calculating the Total Probability:
To find the total probability of drawing 2 green balls first and 2 blue balls second, we multiply the probabilities of each event happening sequentially.
P(2 Green, 2 Blue) = P(2 Green) * P(2 Blue) = (2/15) * (3/14) = 1/35.
Therefore, the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls is 1/35.
To calculate the probability of drawing 2 green balls first, we first need to determine the total number of ways we can draw 2 balls out of 10 (6 blue and 4 green). This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!), where n is the total number of balls and r is the number of balls drawn.
In this case, C(10, 2) = 10! / (2!(10-2)!) = 45.
The number of ways to draw 2 green balls out of 4 is C(4, 2) = 6.
Therefore, the probability of drawing 2 green balls first is 6/45 = 2/15.
Calculating the Probability of Drawing 2 Blue Balls Second:
After drawing 2 green balls, there are now 8 balls remaining in the bag (4 blue and 4 green). We need to determine the probability of drawing 2 blue balls from these 8.
The total number of ways to draw 2 balls out of 8 is C(8, 2) = 28.
The number of ways to draw 2 blue balls out of 4 is C(4, 2) = 6.
Therefore, the probability of drawing 2 blue balls second is 6/28 = 3/14.
Calculating the Total Probability:
To find the total probability of drawing 2 green balls first and 2 blue balls second, we multiply the probabilities of each event happening sequentially.
P(2 Green, 2 Blue) = P(2 Green) * P(2 Blue) = (2/15) * (3/14) = 1/35.
Therefore, the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls is 1/35.
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A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls?
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A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls?.
A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 6 Blue and 4 Green balls. Two successive draws of 2 balls are made without replacement. What is the probability that the first draw will produce 2 Green balls and the second draw will produce 2 Blue balls?.
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