April 2012 question 10

[johnpe21]

Can you please explain how does he derive the probability of function of S? i cant figure it out. He says that s could be 0,1,2,3 or 4. How does this come from ? and hence how does he calculate the function ??

Thanks a lot

 

[bapan]

Hi

Here S = X1 + X2 .. +Xn where Xi is the number of cars involved in i-th accident and n is the number of accidents.

If n = 0, then S = 0 (obvious !)
If n = 1, S can be 1 or 2 i.e. either 1 or 2 cars can be involved in the accident
If n = 2, S can be (1, 1) if 1 car is involved in each accident, (1, 2) or (2, 1) if 1 and 2 cars are involved in either accidents, (2, 2) if 2 cars are involved in each accident. So, S can take value 2, 3 or 4 here.

Thus, possible values of S is 0, 1, 2, 3 or 4

Trust this helps.

 

[Lewin]

Please explain how the probability fuctions have been computed i.e how is p(s=4)=0.2*0.3^2 ?

 

[Lewin]

Tutors?

 

[John Lee]

Tutors?

Apologies for the delay. My colleague who's currently responsible for this forum is on holiday - but I'm aware of this now and will watch this forum!

For S=4 cars total the only combination that produces this is 2 accidents each with 2 cars, ie N=2 and X1 =2 and X2 = 2.

Hence, since they're all independent:

P(S=4) = P(N=2)P(X1=2)P(X2=2) = 0.2×0.3×0.3

 

[Christina]

Tree Diagram

Try drawing out the outcomes in a type of tree diagram - I found that that made the probabilities alot clearer