What is the probability of a student engaging in specific behaviors in a class?

[csc2iffy]

Homework Statement

This is one of my study guide questions and I need a little help

Suppose that in a class of 500 students 210 smoke, 258 drink, 216 snack, 122 smoke and drink, 83 snack and drink, 97 smoke and snack, and 52 do all three. What is the probability that a student:
(a) smokes but doesn't not drink
(b) snacks and drinks, but doesn't smoke
(c) neither smokes or drinks

Homework Equations

The Attempt at a Solution

Sm=smokes
D=drinks
Sn=snacks

(a) Prob(Sm $\cap$ ~D) = P(Sm)-P(Sm$\cap$D = (210/500)-??

 

[lanedance]

have you tried drawing a venn diagram?

 

[csc2iffy]

yes, but I'm getting confused because of the probability part

 

[lanedance]

the probabilty of any portion of the venn diagram is just the number of students in it divided by 500

 

[csc2iffy]

this is my diagram... but how many people are left in c? i feel like this problem is simple but I'm just not seeing it

 

[lanedance]

you should have 3 circles, start filling it form the middle out

you know 52 do all three

and you know 97 smoke and snack

this mean 97-52=45 smoke and snack but do not drink, and so on

 

[csc2iffy]

wow! it says it right in the question..nevermind lol

 

[csc2iffy]

thank you for your help!

 

[csc2iffy]

$\cup$

 

[lanedance]

no worries