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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.

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

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02 May 2012, 14:44

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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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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....

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

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04 Apr 2015, 10:17

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....

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
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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).

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