# Complement question (statistics)

1. Nov 23, 2009

### lom

"the probability to buy a suite is 0.22
the probability to buy a shirt is 0.3
the probability to buy a tie is 0.28
the probability to buy a suite and shirt is 0.11
the probability to buy a suite and tie is 0.14
the probability to buy a tie and shirt is 0.28

what is the probability that the customer will not by anything?"

i was told that the probability that the customer will not by anything
equals the complement of the probability that he buys at least 1 item
why???

as i see it to solve it we need to do
(1-0.11)*(1-0.14)*(1-0.1)=0.68

why am i wrong?

2. Nov 23, 2009

First, iN your approach you are assuming the choices are independent - they may not be.

Second, you are trying to find thechance JUST that group of 3 things; you haven't accounted for the purchase of a subset of them.

Think this way: either some item ispurchased or nothing is -those are complements.

3. Nov 23, 2009

### lom

of course the choises are independent
a shirt differs from a tie etc..

"you are trying to find thechance JUST that group of 3 things; you haven't accounted for the purchase of a subset of them. "
and i dont want to encounter their purchase
thats why i am doing complement

i still cant see my mistake in this way.

i tried to think your way
so i need the complement of
"either some item is purchased"
so we have 7 combinations
_ _ _

for example :
to buy a tie and a suite but not to buy a shirt

etc..

why not
(1-0.11)*(1-0.14)*(1-0.1)=0.68

thats alot
is there easier way?

4. Nov 23, 2009

IF the only two possibilities were to purchase all three items or to purchase nothing, your idea (not the calculation, as you don't know whether the choices to purchase the items are independent) would be correct.

However, there are more than two choices:

* purchase nothing
* purchase exactly one of the three items
* purchase exactly two of the three items
* purchase all of the items

Now do you see why, and where, your approach goes awry?

5. Nov 23, 2009

### lom

why you think that those events are linked??