dave13 wrote:
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies?
1) The probability that she will get a job offer from neither company is 0.3
2) The probability that she will get a job offer from exactly one of the two companies is 0.5
Let’s say Jill is applying to company A and company B. We can create the following equation:
1 = P(offer from only A) + P(offer from only B) + P(offer from both) + P(offer from neither)
We need to determine the probability that she will get a job offer from both companies.
Statement One Alone:The probability that she will get a job offer from neither company is 0.3.
Statement one tells us that P(offer from neither) = 0.3; however, we still need to know P(offer from only A) + P(offer from only B) to determine P(offer from both). Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:The probability that she will get a job offer from exactly one of the two companies is 0.5.
Statement two tells us that P(offer from only A) + P(offer from only B) = 0.5; however, we still need to know P(offer from neither) to determine P(offer from both). We can eliminate answer choice B.
Statements One and Two Together:Using the information in statements one and two, we know the following:
P(offer from neither) = 0.3
P(offer from only A) + P(offer from only B) = 0.5
Thus:
1 = 0.5 + P(offer from both) + 0.3
0.2 = P(offer from both)
Answer: C
it says:
The probability that she will get a job offer from exactly one of the two companies is 0.5 . Doesnt it mean that A company job offer is \(\frac{1}{2}\)and B company job offer is \(\frac{1}{2}\)
Why here A+b equal to 0.5 , and not 0.5+0.5
P(offer from only A) + P(offer from only B) = 0.5pushpitkc are you around ?
Probus maybe you know
Hi
dave13,
Well if you are aware of the two set theory, it would be simple to visualize Set A as Company M and Set B as comapnay N
So in two set theory we have
Only A=a, Only B=b, Both A&B=x, neither=n and total=T.
Where Total= only A + Only B +A&B+ n
T=a+x+b+n
Set A= only A and A&B = a+x
Set B= only B and A&B= b+x
Both A&bB=x
or
you also want to remember the other form.
Total= Set A +Set B -Both A&B +neither
T= (a+x)+(b+x)-x+n
which is precisely
T=a+x+b+n.
Now coming back to this question
We know that total =1 . Why you may ask. Probability of any event occurring lies between o and 1
We generally say Probability of an event happening + probability of event not happening =1
We are supposed to find the value of x. What will help us reach that.
T-a-b-n=x
1-a-b-n=x
or
Set A+Set B+n -Total= Both
Either we are given Set A, & Set B and Neither.
or
We are given the values of only A Only B and neither.
So statements 1: We are given the value of n and but in absence of any other information this no way leads us to our goal.So INSUFFICIENT
So statements 2: This gives us a lot of information about only A=a and only B=b . Great but we do need the value of neither to calculate both. So INSUFFICIENT
Why does this statement give information about only A , Only B. In mathematics OR represents addition , AND represents multiplication. We are told that she gets job offer from exactly one. What are the elements that represent exactly one only a , only b. This means she gets job offer from only a OR she gets jobs offer from only B
then only a or only b=0.5
this means that only a+only b =0.5 Now since we know what all information is given in two statements, surely should we combine them we get the values of only A=a,only B=b, neither =n
from this
1-a-b-n=x
1-(0.5)-(0.3)=x
or x= 0.2
Hence both statements are required to find the value of "BOTH" which is asked in question So C is sufficient to answer the question
Probus
_________________
Probus
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