Oct 22 08:00 AM PDT  09:00 AM PDT Join to learn strategies for tackling the longest, wordiest examples of Counting, Sets, & Series GMAT questions Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 23 12:00 PM EDT  01:00 PM EDT Are you curious about life at Tuck? Join current secondyear students as they share an insiderview of life as a Tuckie. Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Intern
Status: Undergrad
Affiliations: VIT
Joined: 25 Aug 2018
Posts: 9
Location: India
Concentration: General Management, Operations
GPA: 4
WE: Education (Telecommunications)

A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
Updated on: 25 Oct 2018, 01:31
Question Stats:
56% (02:09) correct 44% (02:01) wrong based on 74 sessions
HideShow timer Statistics
A machine consists of three components, which are components X, Y, and Z. These three components operate properly independently of one another. The machine operates properly only when component X operates properly and at least one of components Y and Z operates properly. The probability that component X operates properly is 0.8, the probability that component Y operates properly is 0.4, and the probability that component Z operates properly is 0.3. What is the probability that the machine operates properly? A) 0.096 B) 0.252 C) 0.464 D) 0.583 E) 0.648 In all the Kaplan explanations for probability questions, it always says, "It is easier for us to find the probability of XYZ not occurring". Can anyone explain why that is? Why can't we just find the probability of XYZ actually occurring? For example, in the question above, they tell us outwardly the probability of Components Y and Z operating properly, 0.4 and 0.3 respectively. My inclination is to simply multiply the probability of Component X working (0.8) with the probabilities of Y or Z working, 0.8 * (0.4 + 0.3) = 0.56. While, I know that the incorrect answer, why doesn't this simple approach work? The explanation states that you must first find the probability of Y and Z NOT operating properly, i.e. 1  0.4 = 0.6 1  0.3 = 0.7 Then multiply them to get 0.42 and subtract it from 1 to find the probability of either Y or Z operating properly, which is 0.58. At that point you just multiply 0.58 by 0.8 and the answer is 0.464. If anyone can shed light on this, I'd appreciate it. Thanks everyone!
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by omkarnikte on 25 Oct 2018, 00:40.
Last edited by Bunuel on 25 Oct 2018, 01:31, edited 3 times in total.
Renamed the topic, edited the question, moved to PS forum and added the OA.



Intern
Joined: 22 Aug 2012
Posts: 1

Re: A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
25 Oct 2018, 01:29
[P(x)*p(y)*p(!z) ] + [ P(X)+P(Z)P(!Y)] + [p(x)+p(y)+p(z)] = [0.8*0.4*0.7] + [0.8*0.3*0.6] + [0.8*0.4*0.3] =0.224+0.144+0.096 =0.464 Ans C
Posted from my mobile device



Manager
Joined: 06 Sep 2018
Posts: 72
Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Analyst (Investment Banking)

A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
08 Nov 2018, 03:09
Quote: In all the Kaplan explanations for probability questions, it always says, "It is easier for us to find the probability of XYZ not occurring". Can anyone explain why that is? Why can't we just find the probability of XYZ actually occurring? For example, in the question above, they tell us outwardly the probability of Components Y and Z operating properly, 0.4 and 0.3 respectively. My inclination is to simply multiply the probability of Component X working (0.8) with the probabilities of Y or Z working, 0.8 * (0.4 + 0.3) = 0.56. While, I know that the incorrect answer, why doesn't this simple approach work? The explanation states that you must first find the probability of Y and Z NOT operating properly, i.e. 1  0.4 = 0.6 1  0.3 = 0.7 Then multiply them to get 0.42 and subtract it from 1 to find the probability of either Y or Z operating properly, which is 0.58. At that point you just multiply 0.58 by 0.8 and the answer is 0.464. If anyone can shed light on this, I'd appreciate it. Thanks everyone! If I have understood this correctly, your approach assumes that the other (third) machine never works in each of your scenarios. This is incorrect. Let me explain. 0.8 * (0.4 + 0.3) = 0.8 * 0.4 + 0.8 * 0.3 = A working * B working + A working * C working In these cases, you're not considering the probability of a third machine [C and B respectively] working or not working, therefore, the implicit assumption in your approach is that C always doesn't work in Case 1 (P(C')=1) and B always doesn't work in Case 2 (P(B') = 1). But we know that's not the case because the question defines the possibilities for B and C working. Therefore, it is important to explicitly define the probability of the machine not working or else it defaults to x1 which is wrong. Note that you're also ignoring the event when both B and C work along with A, so the approach is flawed overall.
_________________
The importance of mindset on the GMAT  640 to 690 to 740 (Q49 V42) : https://bit.ly/2R1WaK5



Intern
Joined: 04 Oct 2018
Posts: 6

Re: A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
10 Nov 2018, 02:35
Anyone please help me solve this question.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India

Re: A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
10 Nov 2018, 02:49
omkarnikte wrote: A machine consists of three components, which are components X, Y, and Z. These three components operate properly independently of one another. The machine operates properly only when component X operates properly and at least one of components Y and Z operates properly. The probability that component X operates properly is 0.8, the probability that component Y operates properly is 0.4, and the probability that component Z operates properly is 0.3. What is the probability that the machine operates properly? A) 0.096 B) 0.252 C) 0.464 D) 0.583 E) 0.648 In all the Kaplan explanations for probability questions, it always says, "It is easier for us to find the probability of XYZ not occurring". Can anyone explain why that is? Why can't we just find the probability of XYZ actually occurring? For example, in the question above, they tell us outwardly the probability of Components Y and Z operating properly, 0.4 and 0.3 respectively. My inclination is to simply multiply the probability of Component X working (0.8) with the probabilities of Y or Z working, 0.8 * (0.4 + 0.3) = 0.56. While, I know that the incorrect answer, why doesn't this simple approach work? The explanation states that you must first find the probability of Y and Z NOT operating properly, i.e. 1  0.4 = 0.6 1  0.3 = 0.7 Then multiply them to get 0.42 and subtract it from 1 to find the probability of either Y or Z operating properly, which is 0.58. At that point you just multiply 0.58 by 0.8 and the answer is 0.464. If anyone can shed light on this, I'd appreciate it. Thanks everyone! We are given that Y and Z are independent components so they operate independently. Machine operates if X operates AND (Y or Z operates) P(Machine) = P(X) * P(Y or Z) P (Y or Z) = P(Y)+P(Z)  P(Y and Z) = P(Y) + P(Z)  P(Y)*P(Z) = 0.4 + 0.3  0.4*0.3 = 0.58 P(MAchine) = 0.8*0.58 = 0.464 Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India

Re: A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
10 Nov 2018, 02:52
omkarnikte wrote: In all the Kaplan explanations for probability questions, it always says, "It is easier for us to find the probability of XYZ not occurring". Can anyone explain why that is? Why can't we just find the probability of XYZ actually occurring? For example, in the question above, they tell us outwardly the probability of Components Y and Z operating properly, 0.4 and 0.3 respectively. My inclination is to simply multiply the probability of Component X working (0.8) with the probabilities of Y or Z working, 0.8 * (0.4 + 0.3) = 0.56. While, I know that the incorrect answer, why doesn't this simple approach work? The explanation states that you must first find the probability of Y and Z NOT operating properly, i.e. 1  0.4 = 0.6 1  0.3 = 0.7 Then multiply them to get 0.42 and subtract it from 1 to find the probability of either Y or Z operating properly, which is 0.58. At that point you just multiply 0.58 by 0.8 and the answer is 0.464. If anyone can shed light on this, I'd appreciate it. Thanks everyone! You are right. I wouldn't think in terms of "Not Y and Z" either because calculating P(Y or Z) is easy enough. Note though that P(Y Or Z) is not P(Y) + P(Z). It is P(Y) + P(Z)  P(Y and Z) because P(Y and Z) is double counted (once in P(Y) and once in P(Z)). So you need to remove it out once.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: A machine consists of three components, which are components X, Y, and
[#permalink]
Show Tags
10 Nov 2018, 03:01
A machine consists of three components, which are components X, Y, and Z. These three components operate properly independently of one another. The machine operates properly only when component X operates properly and at least one of components Y and Z operates properly. The probability that component X operates properly is 0.8, the probability that component Y operates properly is 0.4, and the probability that component Z operates properly is 0.3. What is the probability that the machine operates properly?
A) 0.096 B) 0.252 C) 0.464 D) 0.583 E) 0.648
we can solve the problem: P(X)*P(y)*nP(x)+P(x)*P(Z)*nP(y)+P(x)+P(y)+P(z) = (0.8*0.4*0.7)+(0.8*0.3*0.6)+(0.8*0.4*0.3) = 0.224+0.144+0.096 = 0.464, option C




Re: A machine consists of three components, which are components X, Y, and
[#permalink]
10 Nov 2018, 03:01






