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In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512?
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In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one...
Understanding the Problem
In a 3 by 3 grid, we have 9 squares, and each square can be colored either red or blue. We want to find the probability of having at least one 2 by 2 red square.
Total Combinations
- Each square can be colored in 2 ways (red or blue).
- Therefore, the total number of combinations for the 3 by 3 grid is:
- 2^9 = 512 combinations.
Identifying 2 by 2 Red Squares
- A 2 by 2 red square can be positioned in the grid at the following locations:
- Top-left (squares 1, 2, 4, 5)
- Top-right (squares 2, 3, 5, 6)
- Bottom-left (squares 4, 5, 7, 8)
- Bottom-right (squares 5, 6, 8, 9)
- This gives us a total of 4 possible positions for a 2 by 2 red square.
Counting Favorable Outcomes
- For each of the 4 positions, all 4 squares must be red.
- The remaining 5 squares can be colored either red or blue, which gives:
- 2^5 = 32 combinations for the remaining squares.
Calculating Probability
- The total number of favorable outcomes (having at least one 2 by 2 red square) is 4 * 32 = 128.
- Therefore, the probability of getting at least one 2 by 2 red square is:
- 128 / 512 = 1/4.
Final Answer
- The probability of getting a 2 by 2 red square is 128/512, which corresponds to option C: 128/512.
In a 3 by 3 grid, we have 9 squares, and each square can be colored either red or blue. We want to find the probability of having at least one 2 by 2 red square.
Total Combinations
- Each square can be colored in 2 ways (red or blue).
- Therefore, the total number of combinations for the 3 by 3 grid is:
- 2^9 = 512 combinations.
Identifying 2 by 2 Red Squares
- A 2 by 2 red square can be positioned in the grid at the following locations:
- Top-left (squares 1, 2, 4, 5)
- Top-right (squares 2, 3, 5, 6)
- Bottom-left (squares 4, 5, 7, 8)
- Bottom-right (squares 5, 6, 8, 9)
- This gives us a total of 4 possible positions for a 2 by 2 red square.
Counting Favorable Outcomes
- For each of the 4 positions, all 4 squares must be red.
- The remaining 5 squares can be colored either red or blue, which gives:
- 2^5 = 32 combinations for the remaining squares.
Calculating Probability
- The total number of favorable outcomes (having at least one 2 by 2 red square) is 4 * 32 = 128.
- Therefore, the probability of getting at least one 2 by 2 red square is:
- 128 / 512 = 1/4.
Final Answer
- The probability of getting a 2 by 2 red square is 128/512, which corresponds to option C: 128/512.
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In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512?
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In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512?.
In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 3 by 3 grid , there r 9squares of 1 by 1 , we can colour each one block ,either red or blue, find the probability of getting a 2 by 2 red square. A.49\ 512 B.95\512 C.128\512?.
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