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The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?
- a)P=1/3+1/5*3
- b)P=1/5*(1/8-3)
- c)p = (1/3) + (3* 1/5)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The bacteria has the probability of split into 3 and probability to di...
Probability for the bacteria to be dying = 1/3
Hence probability of survival = 1/5
if they survive, they will be split into 3 more bacteria hence, p = (1/3) + (3* 1/5)
Most Upvoted Answer
The bacteria has the probability of split into 3 and probability to di...
Given:
- The bacteria has the probability of splitting into 3.
- The probability of dying is 1/3rd of the total bacteria.
- Let the probability be P.
- Some of them survive with a probability of 1/5.
To find the correct relation, let's break down the problem step by step.
Finding the probability of splitting:
- The bacteria has the probability of splitting into 3.
- This means that for every bacteria, there is a 1/3 probability of it splitting into 3 new bacteria.
- Therefore, the probability of splitting is 1/3.
Finding the probability of dying:
- The probability of dying is 1/3rd of the total bacteria.
- Let's assume there are N bacteria initially.
- The probability of dying for each bacteria is 1/3.
- So, the total probability of dying is (1/3) * N.
Finding the probability of surviving:
- Some of the bacteria survive with a probability of 1/5.
- Let's assume X bacteria survive out of N initial bacteria.
- The probability of surviving for each bacteria is 1/5.
- So, the total probability of surviving is (1/5) * X.
Finding the relation between the probabilities:
- The total initial bacteria N can be split into 3 new bacteria or die.
- Therefore, the total probability of splitting or dying is equal to 1.
- So, we have the equation: (1/3) + (1/3) * N = 1.
- Solving this equation, we get N = 2/3.
- The total surviving bacteria X can come from the initial bacteria or the splitting bacteria.
- Therefore, the total probability of surviving is equal to the sum of surviving from the initial bacteria and surviving from the splitting bacteria.
- So, we have the equation: (1/5) * X + (1/3) * (1/3) * X = 1.
- Substituting the value of N, we get: (1/5) * X + (1/3) * (1/3) * X = 1.
- Simplifying this equation, we get (1/5) * X + (1/9) * X = 1.
- Combining the terms, we get (9/45) * X + (5/45) * X = 1.
- Simplifying further, we get (14/45) * X = 1.
- Dividing both sides by (14/45), we get X = 45/14.
Therefore, the correct relation is:
- p = (1/3) * (3 * (1/5)).
- Simplifying this, we get p = (1/3) * (3/5).
- Further simplifying, we get p = (1/5).
- So, the correct answer is option 'C': p = (1/3) * (3/5).
- The bacteria has the probability of splitting into 3.
- The probability of dying is 1/3rd of the total bacteria.
- Let the probability be P.
- Some of them survive with a probability of 1/5.
To find the correct relation, let's break down the problem step by step.
Finding the probability of splitting:
- The bacteria has the probability of splitting into 3.
- This means that for every bacteria, there is a 1/3 probability of it splitting into 3 new bacteria.
- Therefore, the probability of splitting is 1/3.
Finding the probability of dying:
- The probability of dying is 1/3rd of the total bacteria.
- Let's assume there are N bacteria initially.
- The probability of dying for each bacteria is 1/3.
- So, the total probability of dying is (1/3) * N.
Finding the probability of surviving:
- Some of the bacteria survive with a probability of 1/5.
- Let's assume X bacteria survive out of N initial bacteria.
- The probability of surviving for each bacteria is 1/5.
- So, the total probability of surviving is (1/5) * X.
Finding the relation between the probabilities:
- The total initial bacteria N can be split into 3 new bacteria or die.
- Therefore, the total probability of splitting or dying is equal to 1.
- So, we have the equation: (1/3) + (1/3) * N = 1.
- Solving this equation, we get N = 2/3.
- The total surviving bacteria X can come from the initial bacteria or the splitting bacteria.
- Therefore, the total probability of surviving is equal to the sum of surviving from the initial bacteria and surviving from the splitting bacteria.
- So, we have the equation: (1/5) * X + (1/3) * (1/3) * X = 1.
- Substituting the value of N, we get: (1/5) * X + (1/3) * (1/3) * X = 1.
- Simplifying this equation, we get (1/5) * X + (1/9) * X = 1.
- Combining the terms, we get (9/45) * X + (5/45) * X = 1.
- Simplifying further, we get (14/45) * X = 1.
- Dividing both sides by (14/45), we get X = 45/14.
Therefore, the correct relation is:
- p = (1/3) * (3 * (1/5)).
- Simplifying this, we get p = (1/3) * (3/5).
- Further simplifying, we get p = (1/5).
- So, the correct answer is option 'C': p = (1/3) * (3/5).
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The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer?
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The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer?.
The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?a)P=1/3+1/5*3b)P=1/5*(1/8-3)c)p = (1/3) + (3* 1/5)Correct answer is option 'C'. Can you explain this answer?.
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