- #1
DotKite
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Homework Statement
A large classroom has 100 students. 30 speak spanish, 25 speak italian, and 55 speak neither.
a). how many speak both?
b).A student who speak italian is chosen at random. What is the probability that he/she speaks spanish?
Homework Equations
P(A) = 1 - P(A[itex]^{c}[/itex])
P(U) = 1, where U with the universal set
(A[itex]\cap[/itex]B)[itex]^{c}[/itex] = (A[itex]^{c}[/itex] [itex]\cup[/itex] B[itex]^{c}[/itex])
The Attempt at a Solution
so I assume that when they say 30 speak spanish they mean only speak spanish, and the same for italian.
let S be the set of those who speak spanish and let I be the set of those who speak italian.
P(S-I) = 30/100, P(I-S) = 25/100
P(who speak neither) = 55/100
1-P(who speak neither) = P(S [itex]\cup[/itex] I) = 45/100
THen I thought that you would want to do,
P(S [itex]\cup[/itex] I) - [P(S-I) + P(I-S)] in order to get P(S [itex]\cap[/itex] I) but that comes out to be negative so I am clearly not correct. I do not know what else to do. Been on this problem for a ever now.
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