Question

5. Fill out the blanks in the following table. Note: Ethnicities are the columns and Blood Types are the columns AB Total 0.082 0.008 0.106 0.141 0.200 0.200 0.006 0.020 0.030 0.018 0.215 0.500 Total 0.432 0.091 Events are defined as follows: A [Blood type A), B Ethnicity 1) (Blood type Bl, C -(Ethnicity 3), D- Determine the following a. P(A) b. P(C) C. PA and C) d. P(AlC) e. P(CIA) f. P(B) g. P(BC h. P(D and B)

Answer 1

5)

	O	A	B	AB	Total
1	0.082	0.106	0.008	0.2-0.082-0.106-0.008=0.004	0.2
2	0.3-0.141-0.018-0.006=0.135	0.141	0.018	0.006	1-0.2-0.5=0.3
3	0.215	0.2	0.5-0.215-0.2-0.02=0.065	0.02	0.5
Total	0.432	0.106+0.141+0.2=0.447	0.091	0.03	1

a)

Using the table, $P(A)=0.447$

b)

Using the table, $P(C)=0.5$

c)

Using the table, $P(A\cap C)=0.3$

d)

Using the table, $P(A|C)=\frac{P(A\cap C)}{P(C)}=\frac{0.3}{0.5}=0.6$

e)

Using the table, $P(C|A)=\frac{P(C\cap A)}{P(A)}=\frac{0.3}{0.447}=0.6711$

f)

Using the table, $P(B)=0.091$

g)

Using the table,$P(B^{C})=1-P(B)=1-0.091=0.909$

h)

Using the table,$P(D\cap B^{C})=P(D)-P(D\cap B)=0.2-0.008=0.192$

i)

Using the table,$P(D|B^{C})=\frac{P(D\cap B^{C})}{P(B^{C})}=\frac{0.192}{0.909}=0.211$