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The probability that a radar will detect an object in one cycle is p. The probability that it will be detected in n cycles is
- a)1-pn
- b)1-(1-p)n
- c)pn
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The probability that a radar will detect an object in one cycle is p. ...
1 - prob. than in n cycle sit is not detected,
= 1-(1-p)n
= 1-(1-p)n
Most Upvoted Answer
The probability that a radar will detect an object in one cycle is p. ...
1 - prob. than in n cycle sit is not detected,
= 1-(1-p)n
= 1-(1-p)n
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The probability that a radar will detect an object in one cycle is p. ...
Explanation:
To understand why the correct answer is option B, let's break down the problem step by step.
Probability of not detecting an object in one cycle:
The probability of not detecting an object in one cycle is 1-p. This is because the probability of detecting an object in one cycle is p, so the probability of not detecting it is 1-p.
Probability of not detecting an object in n cycles:
If the probability of not detecting an object in one cycle is 1-p, then the probability of not detecting it in n cycles is (1-p)^n. This is because each cycle is an independent event, and the probability of not detecting the object in each cycle is the same (1-p).
Probability of detecting an object in n cycles:
The probability of detecting an object in n cycles is 1 minus the probability of not detecting it in n cycles. So, the probability of detecting an object in n cycles is 1 - (1-p)^n.
Therefore, the correct answer is option B: 1 - (1-p)^n. This formula gives us the probability of detecting an object in n cycles, taking into account the probability of not detecting it in each cycle.
To understand why the correct answer is option B, let's break down the problem step by step.
Probability of not detecting an object in one cycle:
The probability of not detecting an object in one cycle is 1-p. This is because the probability of detecting an object in one cycle is p, so the probability of not detecting it is 1-p.
Probability of not detecting an object in n cycles:
If the probability of not detecting an object in one cycle is 1-p, then the probability of not detecting it in n cycles is (1-p)^n. This is because each cycle is an independent event, and the probability of not detecting the object in each cycle is the same (1-p).
Probability of detecting an object in n cycles:
The probability of detecting an object in n cycles is 1 minus the probability of not detecting it in n cycles. So, the probability of detecting an object in n cycles is 1 - (1-p)^n.
Therefore, the correct answer is option B: 1 - (1-p)^n. This formula gives us the probability of detecting an object in n cycles, taking into account the probability of not detecting it in each cycle.
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