Because of the increasing nuisance of spam e-mail messages, many start-up companies have emerged to develop e-mail filters. One such filter was recently advertised as being 95% accurate. But what does that mean? Let S denote the event that the message is spam, and let B denote that the filter blocks a message. Using these events and their complements, match each of these four possibilities to their mathematical notation: P (BC|SC) = 0.95 P (SC|BC) = 0.95 P (B|S) = 0.95 P (S|B) = 0.95

Question

Linus

Mathematics

29 March, 13:47

Because of the increasing nuisance of spam e-mail messages, many start-up companies have emerged to develop e-mail filters. One such filter was recently advertised as being 95% accurate. But what does that mean? Let S denote the event that the message is spam, and let B denote that the filter blocks a message. Using these events and their complements, match each of these four possibilities to their mathematical notation: P (BC|SC) = 0.95 P (SC|BC) = 0.95 P (B|S) = 0.95 P (S|B) = 0.95

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Jamie Frye · Answer 1

P (B|S) = 0.95

Step-by-step explanation:

Hello!

A certain company claims that its e-mail filter has 95% accuracy.

Be the events

S: The e-mail is Spam.

B: The filter blocks a message.

If the filter has 95% accuracy it means that it'll block 95% of the spam, another way to put it is that out of 100 spam messages the filter will block 95 of them.

Expressing it in terms of probability we can say that the probability of the filter blocking a message given that it is spam is 0.95, symbolically P (B/S) = 0.95

I hope you have a SUPER day!