What is the probability that two siblings, ages 6 and 8 : GMAT Problem Solving (PS)
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# What is the probability that two siblings, ages 6 and 8

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Joined: 02 May 2012
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What is the probability that two siblings, ages 6 and 8 [#permalink]

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02 May 2012, 13:27
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What is the probability that two siblings, ages 6 and 8, will have the same birthday, assuming neither was born in a leap year?

A. 1/133225
B. 1/365
C. 1/48
D. 1/14
E. 1/2

[Reveal] Spoiler:
A. 1/133225 - I thought this was the correct answer, because from what I understand if we want to find out the prob that BOTH siblings will have the same birthday is much higher than just 1/365. Even though they are independent events, which is 1/365 per time a child is born, in order for both of your child to have the same bday the odds presumably increases. Can someone please correct my logic. Thanks.
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 May 2012, 23:30, edited 1 time in total.
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Re: What is the probability that two siblings, ages 6 and 8 ... [#permalink]

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02 May 2012, 13:44
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The first sibling is born on a given day, that probably is 1/1. The probability of the second having a birthday on the same day is 1/365.

You have to think as the two as independent events. The probably of one person having a birthday on ANY date is 1/1, not 1/365. The second has to match.
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink]

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01 Apr 2015, 04:10
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink]

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02 Apr 2015, 11:50
Hi All,

The explanation offered by pstrench is the most straight-forward way of dealing with this question. The approach taken by iNumbv isn't 'wrong' so much as it's 'incomplete.'

You CAN calculate the probability that two people are BOTH born on any individual day.

eg. What is the probability that they are BOTH born on January 1st?

(1/365)(1/365)

Since we have to account for the FULL YEAR though, we would need to consider all 365 options. You don't really need to write them all out though, since you know that each is the same product. This gives us...

(365)(1/365)(1/365)

The first two parentheses 'cancel out', leaving us with....

1/365

[Reveal] Spoiler:
B

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Joined: 17 Mar 2014 Posts: 238 Location: India Concentration: Operations, Strategy GMAT 1: 670 Q48 V35 GPA: 3.19 WE: Information Technology (Computer Software) Followers: 4 Kudos [?]: 67 [0], given: 175 Re: What is the probability that two siblings, ages 6 and 8 [#permalink] ### Show Tags 04 Apr 2015, 09:17 EMPOWERgmatRichC wrote: Hi All, The explanation offered by pstrench is the most straight-forward way of dealing with this question. The approach taken by iNumbv isn't 'wrong' so much as it's 'incomplete.' You CAN calculate the probability that two people are BOTH born on any individual day. eg. What is the probability that they are BOTH born on January 1st? (1/365)(1/365) Since we have to account for the FULL YEAR though, we would need to consider all 365 options. You don't really need to write them all out though, since you know that each is the same product. This gives us... (365)(1/365)(1/365) The first two parentheses 'cancel out', leaving us with.... 1/365 Final Answer: [Reveal] Spoiler: B GMAT assassins aren't born, they're made, Rich Hi Rich , I am able to follow your solution till you consider both of them to be born on 1st Jan. So each has probability of having bday on 1st jan is = 1/365 Then why we should not multiply these two probabilities ?? as 1/365 * 1/365 I'm a bit confused here ... Aditya _________________ Press +1 Kudos if you find this Post helpful EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8269 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 379 Kudos [?]: 2455 [1] , given: 163 Re: What is the probability that two siblings, ages 6 and 8 [#permalink] ### Show Tags 04 Apr 2015, 11:26 1 This post received KUDOS Expert's post adityadon wrote: EMPOWERgmatRichC wrote: Hi All, You CAN calculate the probability that two people are BOTH born on any individual day. eg. What is the probability that they are BOTH born on January 1st? (1/365)(1/365) GMAT assassins aren't born, they're made, Rich Hi Rich , I am able to follow your solution till you consider both of them to be born on 1st Jan. So each has probability of having bday on 1st jan is = 1/365 Then why we should not multiply these two probabilities ?? as 1/365 * 1/365 I'm a bit confused here ... Aditya Hi Adiya, If you take another look at my explanation, you'll see that I DID multiply (1/365)(1/365)....This is the probability that 2 people are born on January 1st. Since there are 365 days in a normal year and since the question asks for the probability of two people being born on the SAME day (any day, not just on January 1st), we have to think about ALL 365 days. So there are 365 individual calculations that equal (1/365)(1/365). 365(1/365)(1/365) = 1/365 GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: What is the probability that two siblings, ages 6 and 8 [#permalink]

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22 Jan 2016, 08:38
probability of one person born on 1st january is = 1/365
probability of other being born on 1st january is = 1/365

probability of first AND second born on 1st january is = (1/365)*(1/365)

now they can be born on 2nd jan OR 3rd jan OR 4th jan..... OR any day out of the 365 days of the year.

hence probability = (1/365)*(1/365) + (1/365)*(1/365) + (1/365)*(1/365) ........ add 365 times = 365*(1/365)*(1/365) = 1/365
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Re: What is the probability that two siblings, ages 6 and 8   [#permalink] 22 Jan 2016, 08:38
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