65% of the employees in a firm are graduates and 35% did not receive any graduate trainig.
Among the graduates, 40% have an experience of less than 10 years. Similarly, 18% of the non graduate emplyees have an experience of more than 10 years.
The first question is construct the corresponding contignency tables.
answer: i did it like that
GRADUATES NON GRADUATES
EMPLOYESS 65% 35% (total=100)
less thn 10 yrs 40% 25%(total 65)
mre than 10 years 17% 18% (total 35)
The toal of grduates column is 122, for non graduats is 78% for the total column is 200
The second question :what is the probability that an employee chosen randomly is a graduate or has an experience of more than 10 years?
for that second question:should i take 65/200 and 17/200?if yes,should i calculate it in terms of its percentage?? i mean 65/100*200 ??
I interpret the problem different from you. I take
"Among the graduates, 40% have an experience of less than 10 years. "
to mean 40% among the 65% (graduates) have <10 years experience, so (65-26)=39% among the graduates have >10 years experience.
Similarly,
"18% of the non graduate emplyees have an experience of more than 10 years"
would mean 18% of 35%(non-grad) have >10 years experience, or 6.3% of the total have >10 years, leaving (35-6.3)=28.7% have <10 years experience.
The table then becomes:
====G====NG
<10y 26% 28.7% total = 54.7%
>10y 39% 6.3% total = 45.3%
--------65% 35%
We look for Probability of an employee being a graduate given he has more than 10 years experience.
We have learned that conditional probability P(A|B) prob. of A given B
P(A|B)=P(A∩B)/P(B)
So
P(G|>10y)=P(G ∩ >10y)/P(>10y)
=0.39/(0.453)
=0.861 approx.
P(G
To answer the second question, you need to calculate the probability separately for being a graduate and having experience of more than 10 years, and then add those probabilities together.
1) Probability of being a graduate:
The number of employees who are graduates is given as 65% of the total number of employees, which is 200. So, you can calculate it as (65/100) * 200 = 130.
2) Probability of having experience of more than 10 years:
The number of non-graduate employees who have experience of more than 10 years is given as 17% of the total number of employees, which is 200. So, you can calculate it as (17/100) * 200 = 34.
Now, you can add these probabilities together to get the overall probability:
Probability of being a graduate or having experience of more than 10 years = (130 + 34) / 200 = 164 / 200 = 0.82 (or 82%).
So, the probability that an employee chosen randomly is a graduate or has an experience of more than 10 years is 0.82 (or 82%).