Ask your own question, for FREE!
Mathematics 12 Online
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?

OpenStudy (kitkat16):

@kirbykirby can you help?

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?

OpenStudy (kitkat16):

sorry im back

OpenStudy (kitkat16):

ok im following you

OpenStudy (kitkat16):

0.6/0.48 = 0.0125

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 \(P(B\cap S)=P(S \cap B)\)

OpenStudy (kirbykirby):

Your fraction is inverted

OpenStudy (kitkat16):

0.008

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.

OpenStudy (kitkat16):

how do I calculate the 4

OpenStudy (kirbykirby):

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

OpenStudy (kirbykirby):

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

OpenStudy (kirbykirby):

What do you mean by calculate the 4?

OpenStudy (kitkat16):

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

OpenStudy (kitkat16):

not sure how you got the 80 sorry

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%

OpenStudy (kitkat16):

omg sorry 0.8

OpenStudy (kitkat16):

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

OpenStudy (kitkat16):

the word problems confusing more thanks

OpenStudy (kirbykirby):

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

OpenStudy (kirbykirby):

=]

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
Countless7Echos: Ah trying out the whole T.V girl drawing :p (I love drawing eyes)
1 hour ago 7 Replies 5 Medals
kaelynw: starting to draw a hand
1 day ago 16 Replies 2 Medals
Twaylor: Rate it :D (Took 2 days)
2 days ago 7 Replies 0 Medals
XShawtyX: Art, Short Writing Assignment: Imagining Landscapes
1 hour ago 7 Replies 1 Medal
XShawtyX: Chemistry, Help ud83dude4fud83cudffe
3 days ago 13 Replies 1 Medal
kaelynw: tried a lil smt, the arm is off but i like the other stuff
3 days ago 27 Replies 3 Medals
kaelynw: art igg
3 days ago 14 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!