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A binary source generates digits 1 and 0 randomly with equal probability. Then the probability three 1 and four 0 with respect to 7 digits generated by the source is
- a)35/64
- b)35/128
- c)35/256
- d)35/512
Correct answer is option 'B'. Can you explain this answer?
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A binary source generates digits 1 and 0 randomly with equal probabili...
= 35/128
Most Upvoted Answer
A binary source generates digits 1 and 0 randomly with equal probabili...
Given information:
- A binary source generates digits 1 and 0 randomly with equal probability.
To find:
- The probability of getting three 1s and four 0s with respect to 7 digits generated by the source.
Solution:
To find the probability of getting three 1s and four 0s, we need to consider the possible combinations of 1s and 0s that can be generated with respect to the given condition.
Total number of possible outcomes:
The total number of possible outcomes when generating 7 digits from a binary source is 2^7 = 128. This is because each digit can have two possibilities (1 or 0) and there are a total of 7 digits.
Number of favorable outcomes:
To find the number of favorable outcomes where we get three 1s and four 0s, we need to consider the different combinations of arranging these digits.
Arranging the 1s:
The number of ways to arrange three 1s in 7 positions can be calculated using the combination formula:
C(7, 3) = 7! / (3! * (7-3)!) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
Arranging the 0s:
Similarly, the number of ways to arrange four 0s in the remaining 4 positions can be calculated using the combination formula:
C(4, 4) = 4! / (4! * (4-4)!) = 4! / (4! * 0!) = 1
Total number of favorable outcomes:
To find the total number of favorable outcomes, we multiply the number of ways to arrange the 1s and the 0s together:
35 * 1 = 35
Probability:
The probability of getting the desired outcome is the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 35 / 128
Therefore, the probability of getting three 1s and four 0s with respect to 7 digits generated by the source is 35/128, which corresponds to option B.
- A binary source generates digits 1 and 0 randomly with equal probability.
To find:
- The probability of getting three 1s and four 0s with respect to 7 digits generated by the source.
Solution:
To find the probability of getting three 1s and four 0s, we need to consider the possible combinations of 1s and 0s that can be generated with respect to the given condition.
Total number of possible outcomes:
The total number of possible outcomes when generating 7 digits from a binary source is 2^7 = 128. This is because each digit can have two possibilities (1 or 0) and there are a total of 7 digits.
Number of favorable outcomes:
To find the number of favorable outcomes where we get three 1s and four 0s, we need to consider the different combinations of arranging these digits.
Arranging the 1s:
The number of ways to arrange three 1s in 7 positions can be calculated using the combination formula:
C(7, 3) = 7! / (3! * (7-3)!) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
Arranging the 0s:
Similarly, the number of ways to arrange four 0s in the remaining 4 positions can be calculated using the combination formula:
C(4, 4) = 4! / (4! * (4-4)!) = 4! / (4! * 0!) = 1
Total number of favorable outcomes:
To find the total number of favorable outcomes, we multiply the number of ways to arrange the 1s and the 0s together:
35 * 1 = 35
Probability:
The probability of getting the desired outcome is the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 35 / 128
Therefore, the probability of getting three 1s and four 0s with respect to 7 digits generated by the source is 35/128, which corresponds to option B.
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A binary source generates digits 1 and 0 randomly with equal probability. Then the probability three 1 and four 0 with respect to 7 digits generated by the source isa)35/64b)35/128c) 35/256d)35/512Correct answer is option 'B'. Can you explain this answer?
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