A relay has a series of 5 circuits in a line. The even-numbe

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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

by varun289 » Fri Apr 05, 2013 10:15 pm

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Source: Beat The GMAT — Problem Solving | Fri Apr 05, 2013 10:15 pm

bharat.bondalapati: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Apr 05, 2013 11:56 pm; Thanked: 3 times

by bharat.bondalapati » Sat Apr 06, 2013 12:14 am

Hi Varun,

I have a feeling you have not posted the complete information. The questions seems incomplete.
Please post the complete question and i shall be glad to help.

P.S Please thank me if you found my answer helpful

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Sat Apr 06, 2013 1:42 am

Here is the original question.

varun289 wrote:A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 3/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?

Let the circuit series : BCBCB
Probability of the relay failing = Probability that the first combo of CB fails + Probability that second combo of CB fails - Probability that both the combos fails = (3/8)*(3/10) + (3/4)*(2/5) - (3/8)*(3/10)*(3/4)*(2/5) = 9/80 + 6/20 - 27/800 = 90/800 + 240/800 - 27/800 = 303/800

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tarunjohri: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon May 28, 2012 6:18 pm

by tarunjohri » Thu Apr 18, 2013 5:59 am

Hi Anju,

I fail to understand the intersection part.

If we go from either direction, once one pair of CB has failed
the question of second pair would not matter. SO why are you including the
intersection part?

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Thu Apr 18, 2013 7:01 am

tarunjohri wrote:If we go from either direction, once one pair of CB has failed
the question of second pair would not matter. SO why are you including the
intersection part?

Let us indicate a failure by red and success by blue.

So, if the first pair of CB fails, the following scenarios are possible :

1A. BCBCB
1B. BCBCB

And, if the second pair of CB fails, the following scenarios are possible :

2A. BCBCB
2B. BCBCB

Now, 1B and 2B are same scenario.
Hence, if we just add the individual probability of 1st pair of CB failing and 2nd pair of CB failing, we'll end up in considering both failing scenario twice.

That's why we need to subtract the intersection once from the sum of probability.

Hope that helps.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Apr 18, 2013 7:09 am

A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 3/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?

Failure occurs if both circuit2 and circuit3 fail OR if both circuit4 and circuit5 fail

This is an OR probability

P(Event A OR Event B occurs) = P(Event A occurs) + P(Event B occurs) - P(Events A and B both occur)

So, P(complete failure) = P(circuit2 and circuit3 fail OR circuit4 and circuit5 fail)
= P(c2 and c3 fail) + P(c4 and c5 fail) - P(c2 and c3 fail AND c4 and c5 fail)
= (3/8)x(3/10) + (3/4)x(2/5) - (3/8)x(3/10)x(3/4)x(2/5)
= 9/80 + 6/20 - 27/800
= [spoiler]303/800[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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sanaa.rizwan: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Aug 08, 2012 9:00 amFollowed by: 1 member

by sanaa.rizwan » Thu May 23, 2013 9:05 am

P(Event A OR Event B occurs) = P(Event A occurs) + P(Event B occurs) - P(Events A and B both occur)

Can you explain the part in red. The relay fails if event A or B occurs,Why are we subtracting Prob of event A & B

Thanks

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