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There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is?
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There are two boxes containing 5 white and 6 blue balls and 3 white an...
To find the probability of drawing a blue ball from one of the two boxes, we can follow these steps:
Step 1: Identify the Total Number of Balls in Each Box
- Box 1: 5 white + 6 blue = 11 balls
- Box 2: 3 white + 7 blue = 10 balls
Step 2: Calculate the Probability of Selecting Each Box
- Since either box can be selected at random:
- Probability of selecting Box 1 = 1/2
- Probability of selecting Box 2 = 1/2
Step 3: Calculate the Probability of Drawing a Blue Ball from Each Box
- Probability of drawing a blue ball from Box 1:
- Blue balls in Box 1 = 6
- Total balls in Box 1 = 11
- Probability = 6/11
- Probability of drawing a blue ball from Box 2:
- Blue balls in Box 2 = 7
- Total balls in Box 2 = 10
- Probability = 7/10
Step 4: Use the Law of Total Probability
- The total probability of drawing a blue ball, P(Blue), can be calculated as:
P(Blue) = P(Box 1) * P(Blue|Box 1) + P(Box 2) * P(Blue|Box 2)
- Substituting the values:
P(Blue) = (1/2 * 6/11) + (1/2 * 7/10)
= (3/11) + (7/20)
- To combine, convert to a common denominator (220):
= (60/220) + (77/220) = 137/220
Final Probability
- The final probability of drawing a blue ball is 137/220.
Step 1: Identify the Total Number of Balls in Each Box
- Box 1: 5 white + 6 blue = 11 balls
- Box 2: 3 white + 7 blue = 10 balls
Step 2: Calculate the Probability of Selecting Each Box
- Since either box can be selected at random:
- Probability of selecting Box 1 = 1/2
- Probability of selecting Box 2 = 1/2
Step 3: Calculate the Probability of Drawing a Blue Ball from Each Box
- Probability of drawing a blue ball from Box 1:
- Blue balls in Box 1 = 6
- Total balls in Box 1 = 11
- Probability = 6/11
- Probability of drawing a blue ball from Box 2:
- Blue balls in Box 2 = 7
- Total balls in Box 2 = 10
- Probability = 7/10
Step 4: Use the Law of Total Probability
- The total probability of drawing a blue ball, P(Blue), can be calculated as:
P(Blue) = P(Box 1) * P(Blue|Box 1) + P(Box 2) * P(Blue|Box 2)
- Substituting the values:
P(Blue) = (1/2 * 6/11) + (1/2 * 7/10)
= (3/11) + (7/20)
- To combine, convert to a common denominator (220):
= (60/220) + (77/220) = 137/220
Final Probability
- The final probability of drawing a blue ball is 137/220.
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There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is?
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There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is?.
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