Respuesta :
What is the probability that a student who smokes is a graduate student?
What we want to find is: P(G|S)
P(A) = Probability of A
P(A∩B) = Probability of A and B
P(A|B) = Probability of A, given B
U = Undergrad'
G = Graduate
S = Smoker
We just have to use the formula:
P(G|S) = P(G∩S)/P(S)
The statistics given are independent of one another, i.e. they don't affect one another, this means:
P(A∩B) = P(A) * P(B)
So:
P(G∩S) = 0.2 * 0.23 = 0.046
P(S) = (0.2 * 0.23) + (0.8 * 0.15)
= 0.046 + 0.12 = 0.166
Therefore:
P(G|S) = 0.046/0.166 = 0.2771.... ⇒ 0.28 (28%)
A randomly chosen student is more likely to be an undergrad as they comprise 4/5 or 0.8 or 80% of the student body.
Assuming they are a smoker, a randomly chosen student is still more likely to be an undergrad.
We worked out for the first part the probability a student is a graduate and a smoker and found there is only a 28% chance of randomly selecting a graduate from among the smokers.
This means there is a 72% chance you will select an undergrad.
What we want to find is: P(G|S)
P(A) = Probability of A
P(A∩B) = Probability of A and B
P(A|B) = Probability of A, given B
U = Undergrad'
G = Graduate
S = Smoker
We just have to use the formula:
P(G|S) = P(G∩S)/P(S)
The statistics given are independent of one another, i.e. they don't affect one another, this means:
P(A∩B) = P(A) * P(B)
So:
P(G∩S) = 0.2 * 0.23 = 0.046
P(S) = (0.2 * 0.23) + (0.8 * 0.15)
= 0.046 + 0.12 = 0.166
Therefore:
P(G|S) = 0.046/0.166 = 0.2771.... ⇒ 0.28 (28%)
A randomly chosen student is more likely to be an undergrad as they comprise 4/5 or 0.8 or 80% of the student body.
Assuming they are a smoker, a randomly chosen student is still more likely to be an undergrad.
We worked out for the first part the probability a student is a graduate and a smoker and found there is only a 28% chance of randomly selecting a graduate from among the smokers.
This means there is a 72% chance you will select an undergrad.
The probability of a student who smokes is a graduate student is 27.7%
Here, we use Bays theorem of probability.
Bayes' theorem is a way to compute conditional probability
it is used to calculate the probability of an event based on its association with another event.
Probability of event A when event B happen,
[tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]
If Event A and B both are independent.
Then, [tex]P(A\cap B)=P(A)*P(B)[/tex]
Here We represent graduate student by G , under graduate student by U and Student who smoke is by S.
P(Graduate student)= P(G)=1/5 = 0.2
P(under graduate) = P(U)= 4/5 = 0.8
P(Graduate smoke) = 0.23
P(under graduate smoke) = 0.15
We have to find, probability that a student who smokes is a graduate student.
That is, we have to find P(G/S).
[tex]P(G/S)=P(G\cap S)/P(S)[/tex]
Since, Graduate student who smoke is independent.
[tex]P(G\cap S)=P(G)*P(S)=0.2*0.23=0.046[/tex]
[tex]P(S)=(0.2*0.23)+(0.8*0.15)=0.166[/tex]
So, [tex]P(G/S)=\frac{0.046}{0.166}=0.2771\\\\P(G/S)=0.277*100=27.7 percent[/tex]
Learn more:
https://brainly.com/question/10567654
