Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 11 Feb 2008
Posts: 70

Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
Updated on: 02 Feb 2015, 04:43
Question Stats:
74% (01:51) correct 26% (02:04) wrong based on 226 sessions
HideShow timer Statistics
Every trading day, the price of CF Corp stock either goes up by $1 or goes down by $1 with equal likelihood. At the end of 5 trading days, what is the probability that the price of CF Corp stock is up by exactly $3 from its initial price? (A) 1/16 (B) 1/8 (C) 5/32 (D) 9/32 (E) 3/8
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by anaik100 on 27 Jul 2010, 08:41.
Last edited by Bunuel on 02 Feb 2015, 04:43, edited 2 times in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 60647

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
27 Jul 2010, 09:11
anaik100 wrote: Every trading day, the price of CF Corp stock either goes up by $1 or goes down by $1 with equal likelihood. At the end of 5 trading days, what is the probability that the price of CF Corp stock is up by exactly $3 from its initial price? (A) 1/16 (B) 1/8 (C) 5/32 (D) 9/32 (E) 3/8 The price is up by exactly $3 in 5 days means that 4 days it went up (+4$) and one day it went down (1$). UUUUD > \(P(U=4)=C^4_5*(\frac{1}{2})^4*\frac{1}{2}=\frac{5}{32}\). Answer: C. If the probability of a certain event is \(p\), then the probability of it occurring \(k\) times in \(n\)time sequence is: \(P = C^k_n*p^k*(1p)^{nk}\) In our case probability of having 4 days when price went up (4U) and one day when price went down (D): \(n=5\) (5 days); \(k=4\) (4 days when price wen t up); \(p=\frac{1}{2}\) (probability of price going up is 1/2). So, \(P = C^k_n*p^k*(1p)^{nk}=C^4_5*(\frac{1}{2})^4*(1\frac{1}{2})^{(54)}=C^4_5*(\frac{1}{2})^5\) OR: probability of scenario UUUUD is \((\frac{1}{2})^4*(\frac{1}{2})^4=(\frac{1}{2})^5\), but UUUUD can occur in different ways: UUUUD; UUUDU UUDUU UDUDU DUUUU; 5 ways (# of permutations of five letters UUUUD, which is \(\frac{5!}{4!}=5=C^4_5\)). Hence \(P=\frac{5!}{4!}*(\frac{1}{2})^5\). Check this links for similar problems: viewtopic.php?f=140&t=96468&p=742767&hilit=+google#p742767viewtopic.php?f=140&t=56812&hilit=+probability+occurring+timesviewtopic.php?f=140&t=88069&hilit=+probability+occurring+timesviewtopic.php?f=140&t=87673&hilit=+probability+occurring+timesAlso you can check Probability chapter of Math Book for more (link in my signature). Hope it helps.
_________________




Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9142
Location: United States (CA)

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
19 Feb 2018, 10:43
anaik100 wrote: Every trading day, the price of CF Corp stock either goes up by $1 or goes down by $1 with equal likelihood. At the end of 5 trading days, what is the probability that the price of CF Corp stock is up by exactly $3 from its initial price?
(A) 1/16 (B) 1/8 (C) 5/32 (D) 9/32 (E) 3/8 In order to have a net change of +$3, we must have 4 “up” days and 1 “down” day. Thus one of the sequences of 4 ups and 1 down is: up  up  up  up  down or UUUUD Let’s determine the probability of this sequence: P(UUUUD) = (1/2)^5 = 1/32 However, since a sequence of the 4 ups and 1 down (UUUUD) can be arranged in 5C4 = 5!/4! = 5 ways, the overall probability is 5 x 1/32 = 5/32. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15975
Location: United States (CA)

Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
Updated on: 19 Feb 2016, 13:25
Hi pacifist85, The specific details in this question factor in a great deal in how you must go about solving it. We're told that the price of the stock either increases by $1 OR decreases by $1 each day for 5 days. So EVERY DAY the price WILL change. To have a net increase of $3, 3 days of increases will NOT be enough. Here's why: 5 days total 3 days of increases = +$3 BUT the remaining 2 days will then be decreases... 2 days of decreases = $2 Net effect: +$3  $2 = +$1 This is NOT what we're looking for, so 3 days of increases would NOT be enough. With 4 days of increases though... 4 days of increase = +$4 1 day of decrease = $1 Net effect: +$4  $1 = +$3 And then there 5 days of increases, which = +$5 So, to get a net increase of $3, we need 4 days of increases (out of the 5 total days). GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15975
Location: United States (CA)

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
19 Feb 2016, 13:25
HI Nez, Since each day involves either an increase or a decrease, there are 2^5 = 32 possible arrangements. Bruteforcing EVERY one of those 32 options isn't really practical though. If you do a bit of work first to figure out what it would take for a 3 dollar increase to occur (4 increases and 1 decrease), THEN you can brute force the possible options from there. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 400
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
02 Feb 2015, 04:16
Hmmm, I have a very basic problem with this question...
Why is it that if we want the stock to go up exactly 3 points we need it to go up for 4 out of 5 days and not 3? Does it start by zero, so first day is zero, second 1, third 2 and fourth day is 3?
Would it be possible to also solve it using probability?
Thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 60647

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
02 Feb 2015, 04:48
pacifist85 wrote: Hmmm, I have a very basic problem with this question...
Why is it that if we want the stock to go up exactly 3 points we need it to go up for 4 out of 5 days and not 3? Does it start by zero, so first day is zero, second 1, third 2 and fourth day is 3?
Would it be possible to also solve it using probability?
Thank you. It does not matter what is the initial price. We know that every trading day, the price, whatever it is, either goes up by $1 or goes down by $1 and the question asks about the probability that the price is up by exactly $3 from its initial price at the end of 5 trading days.
_________________



Senior Manager
Joined: 15 Oct 2015
Posts: 297
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
19 Feb 2016, 10:45
anaik100 wrote: Every trading day, the price of CF Corp stock either goes up by $1 or goes down by $1 with equal likelihood. At the end of 5 trading days, what is the probability that the price of CF Corp stock is up by exactly $3 from its initial price?
(A) 1/16 (B) 1/8 (C) 5/32 (D) 9/32 (E) 3/8 any brute force method here plzzzzzz?



NonHuman User
Joined: 09 Sep 2013
Posts: 14016

Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
Show Tags
14 Apr 2019, 23:17
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: Every trading day, the price of CF Corp stock either goes up
[#permalink]
14 Apr 2019, 23:17






