Question 1169619: Among the candidates who apply for the post of Senior Accountant, 60% have
more than 10 years of experience and 45% have the qualification of MBA. Of
those candidates who have more than 10 years of experience, 35% do not have
the qualification of MBA.
Given that a candidate does not have the qualification of MBA, what is the
probability that the candidate has more than 10 years of experience?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's solve this problem using conditional probability and Bayes' Theorem.
**Understanding the Problem**
We need to find the probability that a candidate has more than 10 years of experience, given that they don't have an MBA.
**Given Information**
* P(Exp > 10) = 0.60 (60% have more than 10 years of experience)
* P(MBA) = 0.45 (45% have an MBA)
* P(¬MBA) = 1 - P(MBA) = 1 - 0.45 = 0.55 (55% do not have an MBA)
* P(¬MBA | Exp > 10) = 0.35 (35% of those with >10 years experience do not have an MBA)
**Solution**
1. **Find P(Exp > 10 and ¬MBA):**
* We know P(¬MBA | Exp > 10) = 0.35.
* Using the conditional probability formula: P(¬MBA | Exp > 10) = P(Exp > 10 and ¬MBA) / P(Exp > 10)
* P(Exp > 10 and ¬MBA) = P(¬MBA | Exp > 10) * P(Exp > 10) = 0.35 * 0.60 = 0.21
2. **Apply Bayes' Theorem:**
* We want to find P(Exp > 10 | ¬MBA), the probability that a candidate has more than 10 years of experience given they don't have an MBA.
* Bayes' Theorem: P(Exp > 10 | ¬MBA) = P(Exp > 10 and ¬MBA) / P(¬MBA)
* P(Exp > 10 | ¬MBA) = 0.21 / 0.55
* P(Exp > 10 | ¬MBA) ≈ 0.3818
**Final Answer**
The probability that a candidate has more than 10 years of experience, given that they do not have the qualification of MBA, is approximately 0.3818.
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