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During transmission over a communication channel bit errors occurs independently with probability 1/2 . If a block of 3 bits are transmitted the probability of at least one bit error is equal to
- a)1/2
- b)3/2
- c)7/8
- d)5/8
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
During transmission over a communication channel bit errors occurs ind...
(1 - p)n + np{ 1 - p)n-1 = Required probability
(Here, n = no. of bits and p = probability) ∴ Required probability
(Here, n = no. of bits and p = probability) ∴ Required probability
Most Upvoted Answer
During transmission over a communication channel bit errors occurs ind...
Probability of at least one bit error in a block of 3 bits:
To solve this problem, we can use the concept of complementary probability. Let's first calculate the probability of no bit errors in a block of 3 bits.
Probability of no bit errors:
Since the probability of a bit error occurring in a transmission is 1/2, the probability of no bit error occurring in a transmission is 1 - 1/2 = 1/2.
For a block of 3 bits, the probability of no bit errors in all 3 bits is (1/2)^3 = 1/8.
Probability of at least one bit error:
The probability of at least one bit error is the complement of the probability of no bit errors. So, the probability of at least one bit error in a block of 3 bits is 1 - 1/8 = 7/8.
Therefore, the correct answer is option 'C' - 7/8.
Explanation:
In a communication channel, bit errors occur independently with a probability of 1/2. This means that for each bit transmitted, there is a 1/2 probability of it being received incorrectly.
To calculate the probability of at least one bit error in a block of 3 bits, we need to consider all possible combinations of bit errors. There are 2^3 = 8 possible combinations of bit errors in a block of 3 bits.
Out of these 8 combinations, there is only one combination where all 3 bits are received correctly. This gives us a probability of 1/8 for no bit errors.
The remaining 7 combinations have at least one bit error. Therefore, the probability of at least one bit error is 7/8.
Hence, the correct answer is option 'C' - 7/8.
To solve this problem, we can use the concept of complementary probability. Let's first calculate the probability of no bit errors in a block of 3 bits.
Probability of no bit errors:
Since the probability of a bit error occurring in a transmission is 1/2, the probability of no bit error occurring in a transmission is 1 - 1/2 = 1/2.
For a block of 3 bits, the probability of no bit errors in all 3 bits is (1/2)^3 = 1/8.
Probability of at least one bit error:
The probability of at least one bit error is the complement of the probability of no bit errors. So, the probability of at least one bit error in a block of 3 bits is 1 - 1/8 = 7/8.
Therefore, the correct answer is option 'C' - 7/8.
Explanation:
In a communication channel, bit errors occur independently with a probability of 1/2. This means that for each bit transmitted, there is a 1/2 probability of it being received incorrectly.
To calculate the probability of at least one bit error in a block of 3 bits, we need to consider all possible combinations of bit errors. There are 2^3 = 8 possible combinations of bit errors in a block of 3 bits.
Out of these 8 combinations, there is only one combination where all 3 bits are received correctly. This gives us a probability of 1/8 for no bit errors.
The remaining 7 combinations have at least one bit error. Therefore, the probability of at least one bit error is 7/8.
Hence, the correct answer is option 'C' - 7/8.
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