Walden's family is shopping for a reclining chair. The chair the family decided on has a retail price of $800 plus 5% sales tax at
four stores. Each store is offering a different promotion.
Store
A
B
C
D
Promotional Offer
$75 instant rebate
10% off sale
% off sale plus store pays sales tax
"no tax" sale the store pays the tax
5
a
Which store has the best deal?
store A
store B
store C
store D

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