Can i get some help with these porblems? Can it be show in excel with the formul
ID: 3174980 • Letter: C
Question
Can i get some help with these porblems? Can it be show in excel with the formulas showing.
In four neighboring European countries a study on blood type was conducted the numbers of individuals are listed with their blood types and home countries. Complete the "Total" row and column and answer the following questions. How many people who were from Sweden had a "negative" blood type? Calculate the probability that a randomly selected person has a "negative" blood type, given that they were from Sweden. Are the events "from Sweden" and "has a 'negative' blood type" independent? Explain. What is the probability that a randomly selected person has B+ blood? What is the probability that a randomly selected person is from Estonia, given that they have B+ blood? What is the probability that randomly selected person has A+ blood or is from Norway? What is the probability that a randomly selected person has A+ blood and is from Norway? Are these events mutually exclusive? Explain. What is the probability that a randomly selected person has O+ blood or has O- blood? What is the probability that a randomly selected person has O+ and has O- blood? Are events mutually exclusive? Explain.Explanation / Answer
Given,
Blood groups in 4 countries
O+
A+
B+
AB+
O-
A-
B-
AB-
Finland
41
57
23
10
6
8
3
2
150
Estonia
29
31
21
7
5
5
3
1
102
Sweden
38
44
13
6
7
9
2
1
120
Norway
37
45
7
4
6
8
2
1
110
145
177
64
27
24
30
10
5
482
A.a) people from Sweden with -ve blood group are 7+9+2+1
Let, X= people with -ve blood group and
Y= people from Sweden
P(X|Y)=P(XY)/P(Y)
=(19/482)/(120/482)
P(X)=19/120=0.1583 or 15.83%
value of X varies with presence or absence of variable Y, Hence both the events are dependent on each other
A.b) Let X=prob of having B+ blood
P(X)=23+21+13+7/482
P(X)=0.1328 or 13.28%
let Y= selected person is from Estonia
to find, P(Y|X)=P(XY)/P(X)
=(21/482)/(64/482)
=0.3281 or 32.81%
hence the prob is 32.81%
A.c) let A=selected person has A+ blood
B=person is from Norway
P(AUB)=P(A)+P(B)-P(AB)
P(AUB)=177+110-45/482
P(AUB)=0.5021 or 50.21%
hence, P(AUB)=50.21%
P(AB)=45/482
P(AB)=0.0934 or 9.34%
Hence, P(AB)=9.34%
both the events are not mutually exclusive because in case of mutually exclusive events the intersection P(AB) would be zero which is not the case here
A.d) let A=selected person has O+ blood
B= selected person has O- blood
P(AUB)=P(A)+P(B)-P(AB)
=145+24-0/482
=0.35 or 35%
hence, P(AUB)=35%
P(AB)=0/482
Hence, P(AB)=0%
both the events are mutually exclusive events because the intersection P(AB) is zero in this case