18.1k views
0 votes
A and B are two weak students in Mathematics and their chances of solving a problem correctly 1/8 and 1/12, respectively. They are given a problem and they obtain the same answer. If the probability of a common mistake is 1/1001 , then the probability that the answer was correct is

A. 12/13
B. 13/14
C. 14/15
D. 15/16

1 Answer

1 vote

Final answer:

To find the probability that the answer was correct, we can use Bayes' theorem. Given the probabilities of A and B solving the problem correctly, along with the chances of a common mistake, we can calculate the probability that A's answer was correct given that they both obtained the same answer. Using Bayes' theorem, we find that the probability is 12/13.

Step-by-step explanation:

To find the probability that the answer was correct, we need to use Bayes' theorem. Let's define the events:



A: A solves the problem correctly

B: B solves the problem correctly



We are given:

P(A) = 1/8

P(B) = 1/12

P(common mistake) = 1/1001



We want to find P(A|same answer), which represents the probability that A's answer was correct given that they both obtained the same answer.



Using Bayes' theorem, we have:

P(A|same answer) = (P(same answer|A) * P(A)) / P(same answer)



The probability that the answer is the same, given A's answer is correct, can be calculated as:

P(same answer|A) = P(A and B both solve the problem correctly) = P(A) * P(B) = (1/8)(1/12)



The probability that the answer is the same can be calculated as:

P(same answer) = P(A and B both solve the problem correctly) + P(not same answer)

P(not same answer) = P(A solves the problem correctly and B makes a common mistake) + P(B solves the problem correctly and A makes a common mistake)



Since A and B's chances of solving the problem correctly are given, we can calculate P(not same answer):

P(not same answer) = (1/8)(1/1001) + (1/12)(1/1001)



Now we can substitute the values into the equation to find P(A|same answer):

P(A|same answer) = [(1/8)(1/12)] / [(1/8)(1/12) + (1/8)(1/1001) + (1/12)(1/1001)]



Simplifying the expression, we get:

P(A|same answer) = 12/13



Therefore, the probability that A's answer was correct given that they both obtained the same answer is 12/13.

User Brettbuddin
by
8.5k points

No related questions found