OpenStudy (kitkat16):

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?

3 years ago
OpenStudy (kitkat16):

@kirbykirby can you help?

3 years ago
OpenStudy (kirbykirby):

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?

3 years ago
OpenStudy (kitkat16):

sorry im back

3 years ago
OpenStudy (kitkat16):

ok im following you

3 years ago
OpenStudy (kitkat16):

0.6/0.48 = 0.0125

3 years ago
OpenStudy (kirbykirby):

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

3 years ago
OpenStudy (kirbykirby):

Your fraction is inverted

3 years ago
OpenStudy (kitkat16):

0.008

3 years ago
OpenStudy (kirbykirby):

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.

3 years ago
OpenStudy (kitkat16):

how do I calculate the 4

3 years ago
OpenStudy (kirbykirby):

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

3 years ago
OpenStudy (kirbykirby):

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

3 years ago
OpenStudy (kirbykirby):

What do you mean by calculate the 4?

3 years ago
OpenStudy (kitkat16):

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

3 years ago
OpenStudy (kitkat16):

not sure how you got the 80 sorry

3 years ago
OpenStudy (kirbykirby):

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%

3 years ago
OpenStudy (kitkat16):

omg sorry 0.8

3 years ago
OpenStudy (kitkat16):

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

3 years ago
OpenStudy (kitkat16):

the word problems confusing more thanks

3 years ago
OpenStudy (kirbykirby):

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

3 years ago
OpenStudy (kirbykirby):

=]

3 years ago