A certain company has 255 employees. If an employee is to be selected

Total employees = 255...
No other info...
is the the probability less than 1/2 that the employee selected will be a woman who has a college degree?
OR is the # of women with college degree \(< \frac{255}{2} .... < 128\)

lets see the statements-

i) 130 of the company's employees do not have a college degree
Lets look at the MAX probability - All the college degree holders are women...
so Women with college degree = 255-130 = 125 < 128..
So even in the MAX case possible, ans will be YES
Suff..

ii) 125 of the company's employees are men
so the remaining 255-125 = 130 are women..
MAX probability = all 130 are with college degree...
so 130 > 128..... ans is NO
MIN prob = None of these 130 are college holders..
0 < 128... ans is YES.
Different answers possible
Insuff

A
_________________

Given
no of employee= 255
question asked P(W)< 1/2
here P (W) indicated probability of employee selected will be a woman who has a college degree
Statement 1

130 employees do not have a college degree. it means 125 employees have a college degree.
hence total men + women who have a college degree = 125
therefor probability of P(M+W)= 125/255 and is less than 1/2.
so consider the extreme. let us assume all 125 are women even then P(w)< 1/2.
Hence from statement we can give answer P(w)<1/2

Statement 2
no of men in a group =125
but from this we cannot tell about no of women who have college degree.
So this is insufficient.
HenceA is our answer

Ans: A
i) if 130 of 255 employees are those without a college degree => <50% have a college degree => Sufficient
ii) 125 of 255 are male => 130 are female => either possibility exists: possibility that all 130 have a college degree, or possibility that <128 have a college degree. Insufficient.

Therefore, answer = A

Question asks if combined probability is less than .5 ?

--> if we can estabilish that one of the two probability is less than .5 then we know that even 1(full probability) * 0.49(anything less than .5) = less than .5

--> A tells that the probability is less than .5 (255-130=125 and 125/255 is less than .5) -- sufficient
--> B clearly not sufficient

Question stem gives us the number of total employees = 255 and asks us -Is the the probability less than 1/2 that the employee selected will be a woman having a degree?
So we have to find out is the number of women who have a college degree is half of the total employee?
Mathematically speaking --->Number of women \(\frac{255 X 1}{2} <127.5\) ??? (This is the crux of the argument)
Since women cannot be half, the numerical figure has to be <128
The other way to see this problem is \(P(Women with degree) =\frac{(Number of women with degree)}{Total employee} <\frac{1}{2}\)


Statement 1)
130 of the company's employees do not have a college degree
It means that 125 people have college degree (These include both men and women)
Now lets look at the maximum probability that all women have college degree.
Women with college degree = 255-130 = 125 (Meaning All women that have college degree are 125 in number)
Notice how even if ALL the women have college degree, it is still not \(\frac{1}{2}\)
So the probability of being a woman and having a college degree cannot ever be \(\frac{1}{2}\) because \(\frac{125}{255}\)is always less than\(\frac{1}{2}\)
Statement 1 gives a definite NO

SO SUFFICIENT (Now the answer can be only A or D)


Statement 2)
125 of the company's employees are men, Meaning (255-125) = 130 are women.
Lets work with the assumption that all 130 are with college degree
Is 130 < 128 (Remember we got this from Stimulus) ---> No
It can also be interpreted as :- \(Is \frac{130}{255} <\frac{1}{2}\)
The answer is still NO

Now lets again work with the assumption that NONE of 130 are with college degree.
MIN prob = None of these 130 are college holders..
0 < 128----> Yes
It can also be interpreted as :-\(Is \frac{0}{255}<\frac{1}{2}\)
The answer in this case is YES

Statement 2 is not giving definite answers. Sometimes it is YES and sometimes it is NO
Therefore not sufficient (Since B is not sufficient then the combined Option D also goes to garbage bin and only Option A remains)

ANSWER IS A


_________________

A

people who have college degree =120
consider all are woman then also p<1/2

2)no suff
women are 130 maybe or maybe not

Understanding the question
If you look at the 4 possible options that the question stem allows, you will see a Venn Diagram with the following subsets:
- WD: Women Degree
- WN: Women No Degree
- MD: Men Degree
- MN: Men No Degree

The question stem asks whether WD < 0.5, or in other words whether WD < 127.5 (or WD < 128, since humans have to be in integers)

Statement 1
It states that there D = 120 and N = 135. For that reason WD (a subset of D) MUST BE less than 120. Sufficient

Statement 2
It states that M = 125 and W = 130. However, WD (a subset of W) could or could not be less than 128. Not Sufficient.

OA = A

It will be awesome if you can make a venn diagram and attach it with your explanation.
Figures and diagrams always help in understanding the answer much more easily and also the retention of such explanation is higher.



_________________

Tricky one..

Statement 1: 130 i.e. more than half of the total employees (255) don't have college degree.

So even we assume all the other employees i.e. 125 to be women, 125/255 < 1/2.

Statement 2: Similar to the above explanation, this statement is not sufficient, as the probability could be < or > 1/2.

Not getting this one

Let me try helping you out.


Total Employees = 255.

A says 130 donot have the college degree.

=> 255-130 have the college degree = 125.

So, lets say all of these 125 are women.

So, Probability that all of these women have the college degree = MAX probability for women to have the degree = 125/255 <1/2.

Even if I consider that all employees are women, still I will get the max probability for women to have the college degree < 1/2.

Thus, A is sufficient.
_________________

have a look at my post just 3 -4 post earlier to yours ... you will get what the question is asking and how to solve it
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The question here is the number of women who has College Degree > 127. So, let`s call that x, is x >127

________________
Done. Thank you.
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Given: A certain company has 255 employees.
Asked: If an employee is to be selected at random from the company's employees, is the the probability less than 1/2 that the employee selected will be a woman who has a college degree?

(1) 130 of the company's employees do not have a college degree

	Have College degree	Do not have College degree	Total
Men
Women
Total	125	130	255

There is a probability that an employees selected to have a college degree = 125/255 < 1/2
Even if we assume that all employees are women who have college degrees, then also probability that the employee selected will be a woman who has a college degree < 1/2
SUFFICIENT

(2) 125 of the company's employees are men

	Have College degree	Do not have College degree	Total
Men			125
Women			130
Total			255

If we assume that all women employees have college degrees, then probability that the employee selected will be a woman who has a college degree = 130/255 > 1/2
In this case, probability may or may not be <1/2
NOT SUFFICIENT

IMO A
_________________

Given: An employee is randomly selected

What we need to find out: If the probability of selecting a woman with a college degree is less than 1/2

What we know
(i) Total employees
(ii) Probability of selecting a woman with a college degree <= Probability of selecting a woman
(iii) Probability of selecting a woman with a college degree <= Probability of selecting an employee with a college degree

Statement 1 130 of the company's employees do not have a college degree

Probability of selecting an employee with a college degree = (255 - 130)/255 = (125/255) < 127.5/255 or (125/255) <1/2
Therefore, Probability of selecting a woman with a college degree < 1/2

Statement 1 is sufficient

Statement 2 125 of the company's employees are men

Probability of selecting a woman = (255 - 125)/255 = 130/255 > 1/2
Therefore, probability of selecting a woman with a college degree < (some number greater than 1/2)
We cannot conclude whether that number would be greater or lesser than 1/2
Statement 2 is insufficient

Therefore, (A) is the answer
_________________

Correct Option : A

We need to prove : P(W) < P(D) by 50%
We have :
Company : 255 employees. - 50% of 255 is between 127 or 128, which is either Womens or has Degree.


Statement (1) : 130 of the company's employees do not have a college degree : 255 - 130 = 125 Nos
Consider all 125 are women's who has Degree, its still less than 127 or 128 - Condition proved - Sufficient

(2) 125 of the company's employees are men : 255 -125 = 130 Nos
130 Womens are greater than 127 or 128, if all Women have degree, fails to prove the required condition - Not Sufficient, eliminates - B, D, and E.
For C details are not sufficient

Winner A

A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the the probability less than 1/2 that the employee selected will be a woman who has a college degree?

(1) 130 of the company's employees do not have a college degree
(2) 125 of the company's employees are men

(1) we have 255-130=125 people have a college degree, but we do not know how many of them are female. However, we can know the maximum number of female emloyees with degree is 125, so p<=125/255<1/2, Sufficient
(2)we can know there are 130 employees are female, but we cannot deduce how many of them have a degree. Let's say if 125 of them have a degree, then the probability is less than 1/2, but if all of them have a degree, then the probability will greater than 1/2, so this condition is Not Sufficient.

How would the response change if the question asked "greater than 1/2" vs the original question?
See below
A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the the probability greater than 1/2 that the employee selected will be a woman who has a college degree?

(1) 130 of the company's employees do not have a college degree
(2) 125 of the company's employees are men