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?
@kirbykirby can you help?
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?
sorry im back
ok im following you
0.6/0.48 = 0.0125
The next step is just to apply the definition of conditional probability: \[ P(B|S)=\frac{P(B\cap S)}{P(S)}\], recall that \(P(B\cap S)=P(S \cap B)\)
Your fraction is inverted
0.008
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.
how do I calculate the 4
it's just 0.8. I don't know why you are dividing by 100?
if you want as a percentage you can multiply by 100, and write 80%
What do you mean by calculate the 4?
If I do 48/60 =4/5 my choice were 0.80 0.92 0.97
not sure how you got the 80 sorry
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%
omg sorry 0.8
ok I get it. My teacher explained a different way.
the word problems confusing more thanks
Ah well there is more than 1 way to approach this problem!
=]
Join our real-time social learning platform and learn together with your friends!