Quiz question, wondering how to actually solve (intro intro probability)

[rsala004]

Homework Statement

so my professor gave us a little quiz today here's a question i was unsure of how to solve.

probability of engine damage is 0.15
prob of transmission damage is 0.02
prob of both engine and transmission damage is 0.01

what is the prob that a car comes in the shop with engine damage and no transmission damage?
P(E $$\cap$$ T$$^{c}$$)

Homework Equations

The Attempt at a Solution

I solved this by using venn diagrams and i think i may have gotten correct answer, but how would you solve this symbolically, like he wanted it solved.

i got 0.14 which is possibly correct.

thanks a lot

 

[queenofbabes]

I suppose you want equations?

Let E, T refer to engine and transmission such that
P(E) = 0.15, P(T) = 0.02, P(E n T) = 0.01

But P(E) = P(E n T) + P(E n [Tbar]), and you have the first 2 values.

Tbar (written T is a horizontal line on top) is usually called the complement of T, such that P(T) + P(Tbar) = 1

 

[statdad]

For a visual approach, look at the attachment.