Question
Download Solution PDFComprehension
Consider the following for the two (02) items that follow:
The probabilities that A, B and C become managers are 3/10 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively.
If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given,
The probability that A , B , and C become managers are:
The conditional probabilities that the bonus scheme is introduced are:
We need to find the probability that B is the manager given that the bonus scheme has been introduced using Bayes' Theorem:
First, calculate the total probability P(D) that the bonus scheme is introduced:
Substitute the values:
Simplifying:
Find a common denominator (LCD = 90):
Now, use Bayes' Theorem to find P(B|D) :
Simplifying:
The probability that the manager appointed was B , given that the bonus scheme has been introduced, is 5/23.
Hence, the correct answer is Option 1.
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.