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Directions: Solve the problem and select the best of the answer choices given.
At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?
  • a)
    1/12
  • b)
    2/12
  • c)
    5/12
  • d)
    7/12
  • e)
    10/12
Correct answer is option 'E'. Can you explain this answer?
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Directions: Solve the problem and select the best of the answer choice...
The correct response is (E). Remember that the probability of something NOT occurring is 1 – the probability of it occurring. So for this question, we can find the probability that those two doctors WILL be working together, then subtract it from one. Let’s start with the first group. If the first person we chose was from the first group, the odds that the second person would be their partner would be 1/8. This is because every doctor in the first group only has ONE partner, and we’d have 8 people to choose from after picking the first person (out of 9 total). 6/9*1/8 = 6/72 = 1/12.
If the first person we chose was from the second group (probability = 3/9), the odds that the second person would be one of their partners would be 2/8. The numerator is 2 this time because each person in the second group has two partners instead of one. 3/9*2/8 = 6/72 = 1/12.
Since EITHER of these outcomes (picking the first person from the first group OR the second group) produces our desired result, we’ll add these probabilities. 1/12 + 1/12 = 2/12 = 1/6.
Therefore, the probability that the two doctors are NOT working together is 1 – 1/6 = 5/6.
Another way to think of this question is to assign letters to each doctor and group them by clinical trial. So AB, CD, EF are from the first group, and GHI are from the second group. There are 6 ways of choosing a pair that are working together: AB, CD, EF, GH, GI, or HI. And we can quickly use the combination formula to find the total possible ways to choose 2 from 9. 9C2 = 9! / 2! 7! = 9 x 8/2 = 72/2 = 36. 6/36 = 1/6.
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Directions: Solve the problem and select the best of the answer choice...
Solution:

The problem states that there are nine doctors in the medical research lab. Six doctors are working on a clinical trial with exactly one other doctor, and three doctors are working on a clinical trial with exactly two other doctors. We need to find the probability that two randomly selected doctors are not working together on a clinical trial.

Total number of combinations:
To find the total number of combinations, we need to calculate the number of ways to select any two doctors out of nine. This can be calculated using the combination formula, which is given by:

C(n, r) = n! / (r!(n-r)!),

where n is the total number of items and r is the number of items to be selected. In this case, n = 9 and r = 2.

C(9, 2) = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 * 8) / (2 * 1) = 36.

Therefore, there are a total of 36 possible combinations of selecting two doctors.

Cases where two doctors are working together:
Now, let's calculate the number of cases where two doctors are working together on a clinical trial.

Number of cases with two doctors working on a clinical trial with exactly one other doctor:
Since there are six doctors working on a clinical trial with exactly one other doctor, we can select one of these six doctors in C(6, 1) ways. For each doctor, there is exactly one other doctor they are working with. Therefore, the number of cases where two doctors are working together on a clinical trial with exactly one other doctor is 6.

Number of cases with two doctors working on a clinical trial with exactly two other doctors:
Since there are three doctors working on a clinical trial with exactly two other doctors, we can select one of these three doctors in C(3, 1) ways. For each doctor, there are two other doctors they are working with. Therefore, the number of cases where two doctors are working together on a clinical trial with exactly two other doctors is 3 * 2 = 6.

Total number of cases where two doctors are working together:
The total number of cases where two doctors are working together is the sum of the cases from the two categories above, which is 6 + 6 = 12.

Probability of two doctors not working together:
The probability that two doctors are not working together on a clinical trial can be calculated as:

P(not working together) = 1 - P(working together).

P(working together) = Number of cases where two doctors are working together / Total number of combinations = 12 / 36 = 1/3.

P(not working together) = 1 - 1/3 = 2/3.

Therefore, the probability that two randomly selected doctors are not working together on a clinical trial is 2/3, which is option E.
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Directions: Solve the problem and select the best of the answer choices given.At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?a)1/12b)2/12c)5/12d)7/12e)10/12Correct answer is option 'E'. Can you explain this answer?
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Directions: Solve the problem and select the best of the answer choices given.At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?a)1/12b)2/12c)5/12d)7/12e)10/12Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Directions: Solve the problem and select the best of the answer choices given.At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?a)1/12b)2/12c)5/12d)7/12e)10/12Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Solve the problem and select the best of the answer choices given.At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?a)1/12b)2/12c)5/12d)7/12e)10/12Correct answer is option 'E'. Can you explain this answer?.
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