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DotKite
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Homework Statement
A study of texting and driving has found that 40% of all fatal auto accidents
are attributed to texting drivers, 1% of all auto accidents are fatal, and
drivers who text while driving are responsible for 20% of all accidents. Find
the percentage of non-fatal accidents caused by drivers who do not text.
Homework Equations
The Attempt at a Solution
Let T denote texting while driving and let F denote fatal accidents.
P(F|T) = .40
P(F) = .01
P(T) = .2
I guess we are trying to find
p(F[itex]^{c}[/itex]|T[itex]^{c}[/itex]
= (p(F[itex]^{c}[/itex][itex]\bigcap[/itex] T[itex]^{c}[/itex]) / p(T[itex]^{c}[/itex]
We know p(F|T) = p(F[itex]\bigcap[/itex]T) / p(T) = 0.4 => p(F[itex]\bigcap[/itex]T) = 0.08
Also p(F[itex]^{c}[/itex] [itex]\bigcap[/itex]T[itex]^{c}[/itex]) = 1 - p(F[itex]\bigcup[/itex]T)
p(F[itex]\bigcup[/itex]T) = p(F) + p(T) - p(F [itex]\bigcap[/itex]T) = .01 + .2 - .08 = .13
I am going to stop here because when I start plugging in everything I have I wind up with the wrong answer. Is ther an assumption I have wrong or have interpreted, as usual, the problem wrong?