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On the disc shown below, a player spins the arrow twice .The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1?
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On the disc shown below, a player spins the arrow twice .The fraction ...
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On the disc shown below, a player spins the arrow twice .The fraction ...
Problem:
On the disc shown below, a player spins the arrow twice. The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1? Explain in details.
Solution:
To find the probability that the fraction a/b is greater than 1, we need to first determine the possible values of a and b that satisfy this condition.
Step 1: Find the possible values of a
There are 8 numbered sectors on the disc, so there are 8 possible values of a, which are:
1, 2, 3, 4, 5, 6, 7, 8
Step 2: Find the possible values of b
For each value of a, there are 8 possible values of b, which are:
a+1, a+2, a+3, a+4, a+5, a+6, a+7, a (if a+7 exceeds 8, then we simply subtract 8 from it to get the corresponding sector number).
Step 3: Find the number of possible outcomes
There are 8 possible values of a and 8 possible values of b for each value of a, giving a total of 64 possible outcomes.
Step 4: Find the number of outcomes where a/b is greater than 1
For a/b to be greater than 1, a must be greater than b. This means that for each value of a, there are only (a-1) possible values of b that satisfy this condition. Therefore, the total number of outcomes where a/b is greater than 1 is:
1+2+3+4+5+6+7 = 28
Step 5: Find the probability that a/b is greater than 1
The probability that a/b is greater than 1 is the number of outcomes where a/b is greater than 1 divided by the total number of possible outcomes, which is:
28/64 = 7/16
Therefore, the probability that the fraction a/b is greater than 1 is 7/16.
On the disc shown below, a player spins the arrow twice. The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1? Explain in details.
Solution:
To find the probability that the fraction a/b is greater than 1, we need to first determine the possible values of a and b that satisfy this condition.
Step 1: Find the possible values of a
There are 8 numbered sectors on the disc, so there are 8 possible values of a, which are:
1, 2, 3, 4, 5, 6, 7, 8
Step 2: Find the possible values of b
For each value of a, there are 8 possible values of b, which are:
a+1, a+2, a+3, a+4, a+5, a+6, a+7, a (if a+7 exceeds 8, then we simply subtract 8 from it to get the corresponding sector number).
Step 3: Find the number of possible outcomes
There are 8 possible values of a and 8 possible values of b for each value of a, giving a total of 64 possible outcomes.
Step 4: Find the number of outcomes where a/b is greater than 1
For a/b to be greater than 1, a must be greater than b. This means that for each value of a, there are only (a-1) possible values of b that satisfy this condition. Therefore, the total number of outcomes where a/b is greater than 1 is:
1+2+3+4+5+6+7 = 28
Step 5: Find the probability that a/b is greater than 1
The probability that a/b is greater than 1 is the number of outcomes where a/b is greater than 1 divided by the total number of possible outcomes, which is:
28/64 = 7/16
Therefore, the probability that the fraction a/b is greater than 1 is 7/16.
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On the disc shown below, a player spins the arrow twice .The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1?
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On the disc shown below, a player spins the arrow twice .The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1? 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 On the disc shown below, a player spins the arrow twice .The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On the disc shown below, a player spins the arrow twice .The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1?.
Solutions for On the disc shown below, a player spins the arrow twice .The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of sector where the arrow stops after the second spin. On every spin each of the numbered sector has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a\b is greater than 1? in English & in Hindi are available as part of our courses for Class 10.
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