3 Question 5 (4 points)
A teacher is making a VENN diagram of his students. The teacher wants to consider
which students have a pet dog and which have a pet cat. His student Jessica has a
cat and a dog. In which region or regions would this place Jessica in the VENN
diagram shown?
6
CAT
DOG
9
D
12
Region A and C
Region A, B, C
Region B only
Region D only

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative