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Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is?
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Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) ...
Problem Statement:
Consider two identical boxes B₁ and B₂ where the box B(i = 1, 2) contains i² red and 5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B₁, otherwise, two balls are drawn with replacement from the box B₂. The probability that the two drawn balls are of different colors is to be determined.
We are given two identical boxes, B₁ and B₂, which contain different numbers of red and white balls. The number of balls in each box depends on the box number. We are also given a fair die which determines from which box the balls are drawn based on the number of dots shown on the top face.
Let's analyze the problem step by step:
Step 1: Determine the number of red and white balls in each box:
- Box B₁ contains 1² = 1 red ball and 5 - 1 - 1 = 3 white balls.
- Box B₂ contains 2² = 4 red balls and 5 - 2 - 1 = 2 white balls.
Step 2: Determine the probabilities of drawing from each box based on the number of dots on the die:
- If N is even or 5, then two balls are drawn with replacement from box B₁.
- Otherwise, two balls are drawn with replacement from box B₂.
Step 3: Calculate the probability of drawing two balls of different colors:
- If two balls are drawn from box B₁, the probability of drawing a red ball and then a white ball (or vice versa) is given by:
P(different colors | B₁) = P(red, white | B₁) + P(white, red | B₁)
P(different colors | B₁) = (P(red | B₁) * P(white | B₁)) + (P(white | B₁) * P(red | B₁))
P(different colors | B₁) = (1/4 * 3/4) + (3/4 * 1/4)
P(different colors | B₁) = 3/8
- If two balls are drawn from box B₂, the probability of drawing a red ball and then a white ball (or vice versa) is given by:
P(different colors | B₂) = P(red, white | B₂) + P(white, red | B₂)
P(different colors | B₂) = (P(red | B₂) * P(white | B₂)) + (P(white | B₂) * P(red | B₂))
P(different colors | B₂) = (4/6 * 2/6) + (2/6 * 4/6)
P(different colors | B₂) = 4/9
Step 4: Calculate the overall probability of drawing two balls of different colors:
- The probability of drawing from box B₁ is given by:
P(B₁) = P(N is even or 5) = 3/6 =
Consider two identical boxes B₁ and B₂ where the box B(i = 1, 2) contains i² red and 5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B₁, otherwise, two balls are drawn with replacement from the box B₂. The probability that the two drawn balls are of different colors is to be determined.
Analysis:
We are given two identical boxes, B₁ and B₂, which contain different numbers of red and white balls. The number of balls in each box depends on the box number. We are also given a fair die which determines from which box the balls are drawn based on the number of dots shown on the top face.
Let's analyze the problem step by step:
Step 1: Determine the number of red and white balls in each box:
- Box B₁ contains 1² = 1 red ball and 5 - 1 - 1 = 3 white balls.
- Box B₂ contains 2² = 4 red balls and 5 - 2 - 1 = 2 white balls.
Step 2: Determine the probabilities of drawing from each box based on the number of dots on the die:
- If N is even or 5, then two balls are drawn with replacement from box B₁.
- Otherwise, two balls are drawn with replacement from box B₂.
Step 3: Calculate the probability of drawing two balls of different colors:
- If two balls are drawn from box B₁, the probability of drawing a red ball and then a white ball (or vice versa) is given by:
P(different colors | B₁) = P(red, white | B₁) + P(white, red | B₁)
P(different colors | B₁) = (P(red | B₁) * P(white | B₁)) + (P(white | B₁) * P(red | B₁))
P(different colors | B₁) = (1/4 * 3/4) + (3/4 * 1/4)
P(different colors | B₁) = 3/8
- If two balls are drawn from box B₂, the probability of drawing a red ball and then a white ball (or vice versa) is given by:
P(different colors | B₂) = P(red, white | B₂) + P(white, red | B₂)
P(different colors | B₂) = (P(red | B₂) * P(white | B₂)) + (P(white | B₂) * P(red | B₂))
P(different colors | B₂) = (4/6 * 2/6) + (2/6 * 4/6)
P(different colors | B₂) = 4/9
Step 4: Calculate the overall probability of drawing two balls of different colors:
- The probability of drawing from box B₁ is given by:
P(B₁) = P(N is even or 5) = 3/6 =
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Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is?
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Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is?.
Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider two identical boxes B_{1} and B_{2} wherethe box B(i = 1, 2) contains i+ 2 red and5 - i - 1 white balls. A fair die is cast. Let the number of dots shown on the top face of the die be N. If N is even or 5, then two balls are drawn with replacement from the box B_{1} , otherwise,two balls are drawn with replacement from thebox B_{2} The probability that the two drawn balls are of different colours is?.
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