### CFA Practice Question

Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?
A. 0.0164
B. 0.2500
Explanation: This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(pr)[q(n-r)]/r!(n-r)!. Here = 400, r = 2,p = 0.0005 and q = 0.9995. Therefore we have 400!(0.00052)(0.9995398)/2!398! = 0.0164.

User Comment
evica How am I supposed to do 400! on BAII Plus when it does not let me? It shows Error 2, anybody has the same problem?
gruszewski use nCr(p^r)(q^(n-r))
jiyeahoya 399*400/2 *(.0005)^2*(.9995)^2
morpheus918 I don't think we'll have to worry about 400! on June 5th. I think they can test the concept without going that high.
Alastair BAII plus can do nCr without error (eg use the formula button provided).
photoshop 400Combination2 *(0.0005)^2 * (0.9995)^398
creativemny Never underestimate the CFA Institute's ability to make the test challenging.
Spain81 Guys its an easy question.... why you're making it so hard is beyond me. What's 400!/398!... 399*400... duh look at jiyeahoya's post. He does it right except you're supposed to multiply .9995^398 and not to the squard
Murashi just impossible to calculate with a HP12C
Dinosaur theres a choose button on the BAII plus
Xocrevilo Exam technique is, I think, the key to getting questions on binomial probability correct. The variance between the individual answers for binomial probability questions strikes me as being much higher than that for other types of questions. Technique: given the information provided, answer B should strike us as being much too high. However, I admit that it is difficult to rule out C without doing the calc...
visiblebob gruszewski's method works
lpan FYI..

400C2=> 400!/(398!x2!)=(400x399x398!)/(398!x2!)
cancel common factor leaving (400x399)/2 =79800

Finishing the ques..
79800x(0.0005^2)x(0.9995^398)=0.0164
mattg Ipan you are a freakin GENIUS!
moneyguy Thanks, Spain. Really liked the "duh" in your post. Very helpful. I suppose you get them all right, huh?
rencsch excellent!