Help Please!
Out of 100 emails, 60 are spam and 48 of those contain the word buy. Of the remaining 40 emails that are not spam, only 4 emails contain the word buy. Given that an email is spam, what is the probability that it contains the word buy?

Question

Help Please!
Out of 100 emails, 60 are spam and 48 of those contain the word buy. Of the remaining 40 emails that are not spam, only 4 emails contain the word buy. Given that an email is spam, what is the probability that it contains the word buy?

kitkat16 · Answer

@kirbykirby can you help?

kirbykirby · Answer

You can approach this problem in 2 ways:

Method 1 (algebraic way):

Say 
$S$=spam, $\bar{S}$=not spam (maybe you use the notation $S^c$ instead?)
$B$ =contains the word buy

You are given this:
$P(S)=60/100=0.6$
$P(S\cap B)=48/100=0.48$ 
$P(\bar{S}\cap B)=4/100 = 0.04$

And you are asked to find $P(B|S)$
Does this make sense so far?

kitkat16 · Answer

sorry im back

kitkat16 · Answer

ok im following you

kitkat16 · Answer

0.6/0.48 = 0.0125

kirbykirby · Answer

The next step is just to apply the definition of conditional probability:
$$ P(B|S)=\frac{P(B\cap S)}{P(S)}$$, recall that $P(B\cap S)=P(S \cap B)$

kirbykirby · Answer

Your fraction is inverted

kitkat16 · Answer

0.008

kirbykirby · Answer

The other method.. is by trying to use logic. Since the question asked you given that you have an email that is spam (so you are only looking at the 60 spam emails now), what is the probability of those containing the word buy? You want to know how many of the spam emails have the word buy, so this is simply 48/60.

kitkat16 · Answer

how do I calculate the 4

kirbykirby · Answer

it's just 0.8. I don't know why you are dividing by 100?

kirbykirby · Answer

if you want as a percentage you can multiply by 100, and write 80%

kirbykirby · Answer

What do you mean by calculate the 4?

kitkat16 · Answer

If I do 48/60 =4/5
my choice were
0.80
0.92
0.97

kitkat16 · Answer

not sure how you got the 80 sorry

kirbykirby · Answer

it's 0.8

48/60 = 0.8

0.48/0.6 = 0.8

I don't know why you were dividing by 100 to get 0.008 o_O

I say you can get "80" (but relly 80%) by converting your decimal into a percentage by doing 0.8 * 100 --> 80%

0.8 = 80%

kitkat16 · Answer

omg sorry 0.8

kitkat16 · Answer

ok I get it. My teacher explained a different way.

kitkat16 · Answer

the word problems confusing more
thanks

kirbykirby · Answer

Ah well there is more than 1 way to approach this problem!

kirbykirby · Answer

=]