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The chances of A, B, C becoming managers of a Testbook company are 4:2:3. The probability that the bonus scheme will be introduced if A, B, C become manager are 0.3, 0.5, 0.8 respectively.
If the bonus scheme has introduced, what is the probability that A is appointed as the manager of Testbook (answer up to 2 decimal place)?
Correct answer is between '0.26,0.27'. Can you explain this answer?
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The chances of A, B, C becoming managers of a Testbook company are 4:2...
P(X)→ probability that bonus scheme is introduced
P(A) → probability of A being a manager.
P(B) → probability of B being a manager.
P(C) → probability of C being a manager.
P(B) → probability of B being a manager.
P(C) → probability of C being a manager.
P(X) = P (A ∩ X) + P (B ∩ X) + P (C ∩ X)
P(X) = P(A)P(X/A) + P(B)P(X/B) + P(C)P(X/C)
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The chances of A, B, C becoming managers of a Testbook company are 4:2...
Problem: The chances of A, B, C becoming managers of a Testbook company are 4:2:3. The probability that the bonus scheme will be introduced if A, B, C become manager are 0.3, 0.5, 0.8 respectively. If the bonus scheme has introduced, what is the probability that A is appointed as the manager of Testbook (answer up to 2 decimal places)?
Solution:
Step 1: Calculate the probability of A, B, C becoming managers of Testbook company.
Total chances = 4 + 2 + 3 = 9
Probability of A becoming the manager = 4/9
Probability of B becoming the manager = 2/9
Probability of C becoming the manager = 3/9
Step 2: Calculate the probability of the bonus scheme being introduced if A, B, C become managers.
Probability of the bonus scheme being introduced if A becomes the manager = 0.3
Probability of the bonus scheme being introduced if B becomes the manager = 0.5
Probability of the bonus scheme being introduced if C becomes the manager = 0.8
Step 3: Calculate the probability of A being appointed as the manager of Testbook company if the bonus scheme is introduced.
Probability of the bonus scheme being introduced = Probability of A becoming the manager * Probability of bonus scheme being introduced if A becomes the manager
= (4/9) * 0.3
= 0.1333
Probability of B becoming the manager * Probability of bonus scheme being introduced if B becomes the manager = (2/9) * 0.5 = 0.1111
Probability of C becoming the manager * Probability of bonus scheme being introduced if C becomes the manager = (3/9) * 0.8 = 0.2667
Step 4: Calculate the probability of A being appointed as the manager of Testbook company if the bonus scheme is introduced.
Probability of A being appointed as the manager if the bonus scheme is introduced = Probability of A becoming the manager and the bonus scheme being introduced / Probability of the bonus scheme being introduced
= 0.1333 / (0.1333 + 0.1111 + 0.2667)
= 0.2666
Step 5: Round off the answer up to 2 decimal places.
Therefore, the probability of A being appointed as the manager of Testbook company if the bonus scheme is introduced is 0.27 (approx).
Solution:
Step 1: Calculate the probability of A, B, C becoming managers of Testbook company.
Total chances = 4 + 2 + 3 = 9
Probability of A becoming the manager = 4/9
Probability of B becoming the manager = 2/9
Probability of C becoming the manager = 3/9
Step 2: Calculate the probability of the bonus scheme being introduced if A, B, C become managers.
Probability of the bonus scheme being introduced if A becomes the manager = 0.3
Probability of the bonus scheme being introduced if B becomes the manager = 0.5
Probability of the bonus scheme being introduced if C becomes the manager = 0.8
Step 3: Calculate the probability of A being appointed as the manager of Testbook company if the bonus scheme is introduced.
Probability of the bonus scheme being introduced = Probability of A becoming the manager * Probability of bonus scheme being introduced if A becomes the manager
= (4/9) * 0.3
= 0.1333
Probability of B becoming the manager * Probability of bonus scheme being introduced if B becomes the manager = (2/9) * 0.5 = 0.1111
Probability of C becoming the manager * Probability of bonus scheme being introduced if C becomes the manager = (3/9) * 0.8 = 0.2667
Step 4: Calculate the probability of A being appointed as the manager of Testbook company if the bonus scheme is introduced.
Probability of A being appointed as the manager if the bonus scheme is introduced = Probability of A becoming the manager and the bonus scheme being introduced / Probability of the bonus scheme being introduced
= 0.1333 / (0.1333 + 0.1111 + 0.2667)
= 0.2666
Step 5: Round off the answer up to 2 decimal places.
Therefore, the probability of A being appointed as the manager of Testbook company if the bonus scheme is introduced is 0.27 (approx).
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The chances of A, B, C becoming managers of a Testbook company are 4:2:3. The probability that the bonus scheme will be introduced if A, B, C become manager are 0.3, 0.5, 0.8 respectively.If the bonus scheme has introduced, what is the probability that A is appointed as the manager of Testbook (answer up to 2 decimal place)?Correct answer is between '0.26,0.27'. Can you explain this answer?
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