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A and B are two candidates seeking admission to the IIMs. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.9.
- a)No
- b)Yes
- c)Either (a) or (b)
- d)Can’t say
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A and B are two candidates seeking admission to the IIMs. The probabil...
P (Both are selected) = P(A) x P(B) Since P(A) = 0.5, we get 0.3 = 0.5 x 0.6.
The maximum value of P(B) = 0.6.
Thus P{B) = 0.9 is not possible.
The maximum value of P(B) = 0.6.
Thus P{B) = 0.9 is not possible.
Most Upvoted Answer
A and B are two candidates seeking admission to the IIMs. The probabil...
Given information:
- Probability of candidate A getting selected = 0.5
- Probability of both candidates A and B getting selected = at most 0.3
Assumptions:
- The selection of candidates A and B are independent events.
Explanation:
To solve this problem, let's consider the following scenarios:
Scenario 1: If the probability of both A and B getting selected is exactly 0.3, then the probability of A getting selected alone would be (0.5 - 0.3) = 0.2. In this case, the probability of B getting selected would be 0.3.
Scenario 2: If the probability of both A and B getting selected is less than 0.3, let's say x, then the probability of A getting selected alone would be (0.5 - x). In this case, the probability of B getting selected would be x.
Now, let's analyze these scenarios:
1. If the probability of both A and B getting selected is exactly 0.3, then the probability of B getting selected would be 0.3. But the question states that the probability of B getting selected is 0.9, which is not possible in this scenario. Therefore, this scenario is not valid.
2. If the probability of both A and B getting selected is less than 0.3, then the probability of B getting selected would be that value. But the question states that the probability of A getting selected is 0.5. In this case, the probability of B getting selected cannot be 0.9 as it exceeds the probability of A getting selected. Therefore, this scenario is also not valid.
Conclusion:
Based on the above analysis, it can be concluded that it is not possible for the probability of B getting selected to be 0.9. Therefore, the correct answer is option 'A' - No.
- Probability of candidate A getting selected = 0.5
- Probability of both candidates A and B getting selected = at most 0.3
Assumptions:
- The selection of candidates A and B are independent events.
Explanation:
To solve this problem, let's consider the following scenarios:
Scenario 1: If the probability of both A and B getting selected is exactly 0.3, then the probability of A getting selected alone would be (0.5 - 0.3) = 0.2. In this case, the probability of B getting selected would be 0.3.
Scenario 2: If the probability of both A and B getting selected is less than 0.3, let's say x, then the probability of A getting selected alone would be (0.5 - x). In this case, the probability of B getting selected would be x.
Now, let's analyze these scenarios:
1. If the probability of both A and B getting selected is exactly 0.3, then the probability of B getting selected would be 0.3. But the question states that the probability of B getting selected is 0.9, which is not possible in this scenario. Therefore, this scenario is not valid.
2. If the probability of both A and B getting selected is less than 0.3, then the probability of B getting selected would be that value. But the question states that the probability of A getting selected is 0.5. In this case, the probability of B getting selected cannot be 0.9 as it exceeds the probability of A getting selected. Therefore, this scenario is also not valid.
Conclusion:
Based on the above analysis, it can be concluded that it is not possible for the probability of B getting selected to be 0.9. Therefore, the correct answer is option 'A' - No.
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