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What is the probability that two siblings, ages 6 and 8

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iNumbv
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What is the probability that two siblings, ages 6 and 8 [#permalink] New post   Updated on: 03 May 2012, 00:30
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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

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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.
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Originally posted by iNumbv on 02 May 2012, 14:27.
Last edited by Bunuel on 03 May 2012, 00:30, edited 1 time in total.
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pstrench
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Re: What is the probability that two siblings, ages 6 and 8 ... [#permalink] New post   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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Re: What is the probability that two siblings, ages 6 and 8 [#permalink] New post   02 Apr 2015, 12:50
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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:
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B


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

1/365

Final Answer:
Show 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
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink] New post   04 Apr 2015, 12:26
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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
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink] New post   22 Jan 2016, 09:38
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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] New post   01 Nov 2019, 14:55
Hi Bunuel

Can you please help with finding similar higher level (700/750) questions.
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink] New post   06 Nov 2019, 02:14
Hey, my approach was:
1. P(e) = 365 x (as giving 365 options for b'day of 1st person, for our event to occur, the other person is left with only 1 option)
2. P(total) = 365x365
3. P = 365/(365x365) = 1/365

I am only confused here, as to why the order is not important.
P(e) should be = 365x1 + 1x365 = 365x2

Can anyone please clarify?
Thanks in advance.
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink] New post   06 Mar 2022, 11:34
I got this correct but is my logic for why A is incorrect appropriate? 1/365 x 1/365 is simply the odds that 2 children happen to born on the exact same date/year but since we know they are different ages, we can't use this probability logic so it's just simply 1/365?
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Re: What is the probability that two siblings, ages 6 and 8 [#permalink]
06 Mar 2022, 11:34
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