Question

Consider the Venn diagram below. The numbers in the regions of the circle indicate the number of items that belong to that region.

Determine
n(A)
n(B)
P(A)
P(B)
P(A|B)
P(B|A)
(Points : 6)

Answer 1

what is the number value of circle A? n(A)

what is the number value of circle B? n(B)

Answer 2

A = 60 and B= 30

Answer 3

close, we want the total value within circle A, so add 50 to that

and same concept on B, so add 50 to it too

Answer 4

60+50= 110 and 50 + 50 =100

Answer 5

nA = 60+50 = 110

nB = 30+50 = 80

for the probability parts, we need the total value of the system
so 60+50+30 = 140 right?

Answer 6

oh I should had add 30 with 50 got it

Answer 7

P(A) is probability of A, so nA/total system value

same concept on P(B) but using nB

Answer 8

ok

Answer 9

P(A) = 110/140

P(B) = 80/140

this look right so far?

Answer 10

yes

Answer 11

as a side note; notice that 110 + 80 is bigger than 140, this tells us that A and B are sharing parts

Answer 12

P(A|B) reads as probability of A given that we have the set of B

there are 50 As in the set of B. that works out to 50/80

Answer 13

ok

Answer 14

P(B|A) is the same concept; there are 50Bs in the set of A; so thats 50/110

Answer 15

the math set up is for P(x|y) is\[\frac{P(x~and~ y)}{P(y)}\]
sooo
\[P(A|B)=\frac{P(A~and~ B)}{P(B)}=\frac{50/140}{80/140}=
frac{50}{80}\]

Answer 16

\[\frac{50}{80}\]latex failed lol

Answer 17

I see thank you

Answer 18

good luck :)