SOLUTION: 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 mo

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.

RELATED QUESTIONS
Suppose that an admission test for a certain university is designed so that the... (answered by stanbon,ewatrrr)

Ten candidates apply for a job and are separately interviewed. Based on past experience,... (answered by ewatrrr,Timnewman)

At a certain non-profit organization, % of employees are college graduates and % of... (answered by stanbon)

I am really struggling with this one and could use some help. At a certain non-profit... (answered by Boreal)

Ive Been struggling with this, any help is greatly appreciated :) At a certain... (answered by edjones)

It is estimated that 60% of the candidates who took an aptitude test passed. If 800 of... (answered by Boreal)

Out of 8000 candidates , 60% were boys.if 80% boys and 90% of the girls passedthe exam,... (answered by dkppathak)