Probability - A and B are two weak students

In summary, A and B are two weak students in Mathematics with a 1/8 and 1/12 chance of solving a problem correctly. The probability of them making a common mistake is 1/1001 and they obtain the same answer. By Baye's theorem, the chance that their answer is correct is 1000/1077.
  • #1
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Probability - A and B are two weak students...

Homework Statement



A and b are two weak students in Mathematics. The chances of their solving a problem correctly is 1/8 and 1/12. The probability of them making a common mistake is 1/1001 and they obtain the same answer. Find the chance that their answer is correct.


The Attempt at a Solution



Let E1 be the event that A and B solve correctly
E2 be the event that A and B solve incorrectly.
K be the event that they obtain same answer.

P(E1) = 1/8 x 1/12
P(K/E1)= 1000/1001
P(E2) = 7/8 x 11/12
P(K/E2) = 1/1001

Now by Baye's theorem,

P(E1/K) = P(E1)xP(K/E1)/...

I got the answer as 1000/1077
The answer given is
13/14

There is a very very small difference in two answers.They are correct upto 3 decimal places.

Please tell me where is my mistake.
 
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  • #2


If I understand correctly, P(K/E1) = 1. If they both get the correct answer, they get the same correct answer.
 
Last edited:
  • #3


You are right. I got it.
Thank you verymuch!
 

1. What is the probability that both A and B will pass the exam?

The probability of both A and B passing the exam depends on their individual abilities and the difficulty level of the exam. Without knowing these factors, it is impossible to determine an exact probability. However, if we assume that A and B have equal chances of passing and the exam is of moderate difficulty, the probability of both passing would be approximately 25% (assuming a 50% pass rate for each student).

2. What is the probability that at least one of them will pass the exam?

The probability of at least one of them passing the exam can be calculated by finding the complement of the probability that both will fail. Assuming an equal chance of passing for A and B, the probability of at least one of them passing would be approximately 75% (assuming a 50% pass rate for each student).

3. Can we predict with certainty that one of them will pass the exam?

No, we cannot predict with certainty that one of them will pass the exam. Probability is based on chance and there is always a possibility that both A and B will fail the exam.

4. How can we improve the chances of A and B passing the exam?

The best way to improve the chances of A and B passing the exam is for them to study and prepare thoroughly. Additionally, they can seek help from a tutor or study group, practice past exams, and identify their weaknesses to focus on improving them.

5. Is there a correlation between A and B's performance on the exam?

Without more information, it is difficult to determine if there is a correlation between A and B's performance on the exam. It is possible that they have similar abilities and study habits, but it is also possible that they have completely different strengths and weaknesses. Evaluating their individual performances would provide a better understanding of any potential correlation.

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