2007 EXAM 1 Q11 b help urgent :(!

[ArthurJ]

0.4 / answer to part a.

I dont understand why it should be 0.32 on top!

Ive looked at solutionions , and worked solutions but it just dosnt make sence to me
Can someone please explain! !

Much appreciated!

Link to exam : http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007mmCAS1-w.pdf
Q 11 b

[RKTR]

Pr(A l B)= Pr(A n B) / Pr(B)
     
Lets say A=fine weather, B = departs on time

so Pr(A n B) = 0.4 x 0.8 =0.32
 then continue

[ahat]

Look at the solution I've attached

The top of the conditional probability equation [Pr(F|O)] is going to be the intersection between Fine weather (F) and the Departing on Time (O). The only branch that corresponds to this is F --> A (have a look at the solution). Looking at the branches, this is 0.4 x 0.8 = 0.32. Hope this helps
Remember, always draw a diagram! Even if it's a cat or whatever - diagrams are of paramount importance!

Edit: thought I might explain it further

Like RKTR said

Pr(A l B)= Pr(A n B) / Pr(B)

You instantly know that it's going to conditional probability because the question says "given that". I've explained the intersection. The denominator, Pr(B) or according to my work Pr(O) is all of the probability that the flight departs on time, good or bad weather, from part a.

Remember, after you see "given that" - look at your formula sheet for the conditional prob. equation if you can't remember.